
            DELUXE PAINT
  To create beautiful pictures on your computer's screen, get a 
program called Deluxe Paint ___ or one of its cousins.
  Deluxe Paint was invented in California by Dan Silva in 1985. 
Then he invented an improved version (Deluxe Paint 2). Then he 
developed a further improvement (Deluxe Paint 3), which included 
advanced graphics tricks and also animation. His programs all ran 
on the Commodore Amiga. They were published by Electronic Arts.
  An Electronic Arts employee ___ Brent Iverson ___ developed an 
IBM version of Deluxe Paint 2. Then another Electronic Arts 
employee ___ Steve Shaw ___ developed an IBM version of Deluxe 
Paint 3 and called it Deluxe Paint Animation. He also invented a 
lesser version called Deluxe Paint 2 Enhanced, which includes all 
the features of Deluxe Paint 3 except animation.
  Electronic Arts also developed an Apple 2GS version of Deluxe 
Paint 2.
  Electronic Arts also sells several paint programs for the Mac: 
Studio 1 has animation but no color; Studio 8 and Studio 32 have 
color but no animation. They were all developed by an independent 
group of French programmers inspired by Dan Silva.
  In this chapter, I'll concentrate on the IBM versions. Each IBM 
version requires 640K of RAM and a mouse.

        Choose an IBM version
  Which IBM version should you buy ___ Deluxe Paint 2, Deluxe 
Paint 2 Enhanced (which should be called Deluxe Paint 2), or 
Deluxe Paint Animation (which should be called Deluxe Paint 3)?
  Intelligence Deluxe Paint Animation understands more commands 
than the other versions, and it's the only version that produces 
animation.
  Price Deluxe Paint 2 has been included free with many computers 
and software packages. That's because it's considered obsolete! 
Discount dealers sell Deluxe Paint 2 Enhanced and Deluxe Paint 
Animation for about $100 each.
  Hard disk Deluxe Paint 2 Enhanced and Deluxe Paint Animation 
require a hard disk. If you don't have a hard disk, you must buy 
Deluxe Paint 2.
  VGA Deluxe Paint Animation requires a VGA (or MCGA) video card. 
If your video card is worse than that ___ if you have just EGA, 
CGA, or Hercules ___ you must buy Deluxe Paint 2 or Deluxe Paint 
2 Enhanced.
  High resolution Unfortunately, Deluxe Paint Animation operates 
just in low resolution (320-by-200). (Instead of using RAM to 
store higher resolution, it uses RAM to store your animation.) If 
you insist on full VGA resolution (640-by-480), buy Deluxe Paint 
2 or Deluxe Paint 2 Enhanced. To operate in Super VGA resolution 
(800-by-600 or 1024-by-768), you must buy Deluxe Paint 2 
Enhanced.
                                         Summary Deluxe Paint 2 
is obsolete. Use it only if you get it free or you're broke or 
you lack a hard disk.
                                         If your computer has a 
poor video card (Hercules monochrome, CGA, or EGA), get Deluxe 
Paint 2 Enhanced.
                                         If your computer has a 
good video card (MCGA, VGA, or Super VGA), get either Deluxe 
Paint Animation or Deluxe Paint 2 Enhanced. Deluxe Paint 
Animation offers animation, but Deluxe Paint 2 Enhanced offers 
higher resolution.
                                         Assumption In the rest 
of this section, I assume you're using Deluxe Paint 2 Enhanced or 
Deluxe Paint Animation.

                                               Copy to the hard disk
                                         When you buy Deluxe 
Paint 2 Enhanced or Deluxe Paint Animation, you get four 5-inch 
floppies and two 3-inch floppies.
                                         Here's how to copy the 
5-inch floppies to your hard disk. (Copying the 3-inch floppies 
is similar.)
                                         Turn on the computer 
without any floppy in drive A. When you see the C prompt, put the 
PROGRAM Disk into drive A and type ``a:''. The computer will 
display an A prompt.
                                         Type ``install''. The 
computer will say ``Installation''.
                                         If you're using Deluxe 
Paint Animation, press ENTER twice. If you're using Deluxe Paint 
2 Enhanced instead, press ENTER once, then type ``dp'' (so the 
screen says ``dp'' instead of ``DPAINT''), then press ENTER 
again.
                                         When the computer tells 
you, put the other three disks in drive A and press ENTER.
                                         The computer will say, 
``Installation Complete!'' (Then if you're using Deluxe Paint 2 
Enhanced, do this: type ``century'', press ENTER, and wait for 
the computer to copy fonts to the hard disk.)
                                         Turn off the computer, 
so you can start fresh.

                                               Run the paint program
                                         To start using the paint 
program, turn on the computer without any floppy in drive A.
                                         To do Deluxe Paint 
Animation, type ``do da''. To do Deluxe Paint 2 Enhanced, type 
``do dp''.
                                         (That ``do'' method 
works if you put the DO.BAT file onto your hard disk as I 
recommended in the MS-DOS chapter. If you have not put DO.BAT 
onto your hard disk, do Deluxe Paint Animation by typing ``cd 
da'' and then ``da''; do Deluxe Paint 2 Enhanced by typing ``cd 
dp'' and then ``dp''.)
         Choose a video mode
  If you're using Deluxe Paint 2 Enhanced, you must choose a 
video mode. (If you're using Deluxe Paint Animation, you don't 
have to choose a video mode, and you can skip ahead to the next 
section.)
  Deluxe Paint 2 Enhanced shows you this list of video modes:
a. CGA           320 x 200    4 colors
b. CGA           640 x 200    2 colors

c. EGA           320 x 200   16 colors
d. EGA           640 x 200   16 colors
e. EGA           640 x 350   16 colors

f. MCGA          320 x 200  256 colors
g. MCGA          640 x 480    2 colors

h. VGA           320 x 200   16 colors
i. VGA           640 x 200   16 colors
j. VGA           640 x 350   16 colors
k. VGA           640 x 480   16 colors

l. Hercules      720 x 348    2 colors

m. Tandy         320 x 200   16 colors

o. Amstrad       640 x 200   16 colors

p. Extended VGA  640 x 400  256 colors
q. Extended VGA  640 x 480  256 colors
r. Extended VGA  800 x 600    2 colors
s. Extended VGA  800 x 600   16 colors
t. Extended VGA  800 x 600  256 colors
u. Extended VGA 1024 x 768    2 colors
v. Extended VGA 1024 x 768   16 colors
  Type a letter from ``a'' to ``v''. Here's which letter to type:
Video you boughtType this letter
Hercules monochrome``l''
CGA           ``a'' for lots of colors, ``b'' for high resolution
EGA           ``e''
MCGA          ``f'' for lots of colors, ``g'' for high resolution
VGA           ``f'' for lots of colors, ``k'' for high resolution
  A plain VGA system is limited to 640-by-480 resolution and has 
a 256K video RAM. If your VGA system can handle higher resolution 
or has extra video RAM, you have extended VGA, which lets you 
type these letters instead:
Extended VGA you got
ResolutionVideo RAMType this letter
640-by-480512K  ``q'' for lots of colors, ``k'' for high res.

800-by-600256K  ``f'' for lots of colors, ``s'' for high res.
800-by-600512K  ``t''

1024-by-768256K ``f'' for lots of colors, ``u'' for high res.
1024-by-768512K ``t'' for lots of colors, ``v'' for high res.
  If you choose a letter near the end of the alphabet (``p'' 
through ``v'', you face two complications:
The computer might say, ``Specify which card is active''. To 
reply, press the SPACE bar, look at the menu of VGA card 
manufacturers, and type your manufacturer's code letter. (If your 
VGA card is manufactured by a company that's not on the menu, try 
pretending that your VGA card is an AST VGA Plus, which handles 
video modes q and r.)

The computer might say, ``Not enough memory''. That means your 
computer doesn't have enough expanded RAM. Choose a different 
letter instead.

                                                  Move the mouse
                                         Look at the computer's 
mouse. The mouse's tail is a cable that runs from the mouse to 
the computer. The area where the tail meets the mouse is called 
the mouse's ass.
                                         The mouse's underside 
___ its belly ___ has a hole in it, and a ball in the hole.
                                         Put the mouse on your 
desktop and directly in front of you. Make the mouse lie flat (so 
its ball rubs against the desk). Make the mouse face you so you 
don't see its ass.
                                         In the middle of the 
screen, you'll see a cross, which is called the mouse pointer.
                                         Move the mouse across 
your desk. As you move the mouse, remember to keep it flat and 
facing you. As you move the mouse, the cross moves also.
                                         If you move the mouse to 
the left, the cross moves to the left. If you move the mouse to 
the right, the cross moves tot he right. If you move the mouse 
toward you, the cross moves down. If you move the mouse away from 
you, the cross moves up.
                                         Practice moving the 
cross by moving the mouse. Remember to keep the mouse facing you 
at all times.
                                         If you want to move the 
cross far and your desk is small, move the mouse until it reaches 
the desk's edge; then lift the mouse off the desk, lay the mouse 
gently on the middle of the desk, and rub the mouse across the 
desk in the same direction as before.

                                                  Draw a squiggle
                                         On the top of the mouse, 
you'll see 2 or 3 rectangular buttons you can press. The main 
button is the one on the left.
                                         The middle of the screen 
is a white, rectangular area that's huge: it consumes most of the 
screen. That area is called the painting area. It's where you 
draw your pictures.
                                         Try this experiment. Put 
the cross in the middle of the screen, in the middle of the 
painting area. While holding down the mouse's left button, move 
the mouse. That activity ___ moving the mouse while holding down 
the mouse's left button ___ is called dragging. As you drag, 
you'll be drawing a squiggle.
                                         For example, try drawing 
a smile. To do that, put the cross where you want the smile to 
begin (at the smile's upper-left corner), the depress the mouse's 
left button while you draw the smile. When you finish drawing the 
smile, lift the mouse's button. Then draw the rest of the face!
            Click an icon
  At the screen's right edge, you see these pictures:
                  One-Dot BrushSquiggle
                  Line        Arc
                  Filled RectangleFilled Circle
                  Filled PolygonFilled Blob
                  Fill        Spray
                  Brush PickupText
                  Grid        Perspective
                  Magnify     Hand
                  Color PickupSymmetry
                  Undo        Clear
                  Gradient    Pattern

                  Color Indicator



                  Color Palette




Those pictures are called icons (or tools).
  Try this experiment: move the mouse pointer (the cross) to 
those icons. When the cross reaches those icons, the cross turns 
into an arrow.
  Line Here's how to draw a line that's perfectly straight.
  Move the mouse pointer until it turns into an arrow, and the 
arrow's tip is in the middle of the Line icon. Then tap the 
mouse's left button. (That's called clicking the Line icon.)
  Then put the mouse pointer in the middle of the screen, in the 
middle of the painting area, where you want the line to begin. 
Drag to where you want the line to end (by moving there while 
holding down the mouse's left button).
  The line you desired will appear!
  Practice drawing lines. When you finish drawing lines and want 
to draw squiggles instead, click the Squiggle icon. (Since the 
Squiggle icon looks like a paintbrush, it's also called the 
Freehand Brush icon).
  Practice! Draw lines, then squiggles, then lines, then 
squiggles. When you feel comfortable, explore the following 
icons, which are more advanced. . . .  
  Arc To draw an arc (a smooth curve), click the Arc icon (which 
is also called the Curve icon). Then put the mouse pointer in the 
painting area, where you want the arc to begin, and drag to where 
you want the arc to end. Lift your finger off the mouse's button, 
move the mouse until the arc has the curvature you wish, then 
click.
  Undo If you make a mistake, click the Undo icon. That makes the 
computer erase the last object you drew (or undo your last 
activity). The screen will look the same as before you drew that 
object (or did that activity).
  Clear To erase everything you drew on the screen (so the screen 
becomes white and you can start over), click the Clear icon 
(which says CLR). If you're using Deluxe Paint Animation, you 
must then press ENTER.
                                         Color Palette Normally, 
the computer draws black shapes (on a white background). To draw 
in a color other than black, look at the Color Palette icon 
(which is divided into many colors), and click the color you 
want. The color you choose is called the foreground color.
                                         For example, to draw a 
blue object, do this: click blue, then draw the object. To erase 
part of an object, do this: click white, then cover the object by 
drawing with white paint.
                                         If you're using Deluxe 
Paint 2 Enhanced and chose a 2-color video mode, the only colors 
in the palette are black and white.
                                         If you're using Deluxe 
Paint Animation (or Deluxe Paint 2 Enhanced in a 256-color mode), 
the Color Palette icon shows just some of the colors. To see 
other colors, repeatedly click the Right Arrow icon (at the 
screen's bottom right corner). To go back to the colors you were 
seeing before, click the Left Arrow icon. When you see your 
favorite color, click it.
                                         Color indicator In the 
middle of the Color Indicator icon, you see the color that you 
picked to be the foreground color.
                                         Color pickup Suppose 
you've drawn a picture, and one of the colors you've used is so 
nice that you want to use it again. Click the Color Pickup icon 
(which looks like an eyedropper that soaks up ink), then click 
your picture's middle, where you used that color. That color will 
become the foreground color.
                                         Filled rectangle To draw 
a rectangle whose sides are perfectly straight, and whose middle 
is filled in, click the Filled Rectangle icon. Then put the mouse 
pointer in the painting area, where you want the rectangle's top 
left corner to be. Drag to where you want the rectangle's 
opposite corner.
                                         Filled circle To draw a 
circle whose middle is filled in, click the Filled Circle icon. 
Then put the mouse pointer in the painting area, where you want 
the circle's center to be. Drag until the circle is as big as you 
wish.
                                         Filled polygon To draw a 
polygon whose middle is filled in, click the Filled Polygon icon. 
Then click in the painting area, where you want the polygon's 
first corner to be.
                                         Click where you want the 
polygon's second corner to be. Presto ___ the computer draws a 
line from the first corner to the second corner!
                                         Click where you want the 
polygon's third corner to be. The computer draws a line from the 
second corner to the third corner.
                                         Keep clicking, until 
you've clicked all the corners. Then press the SPACE bar, which 
makes the computer draw a line from the last corner back to the 
first corner and fill in the polygon.
                                         Filled blob To draw a 
blob (lumpy circle) whose middle is filled in, click the Filled 
Blob icon (which is also called the Filled Freehand Shape icon). 
Then put the mouse pointer in the painting area, where you want 
the blob to begin. Drag in a circular motion (so you're drawing a 
lumpy circle). When you lift your finger from the mouse's button, 
the computer completes the circular shape (by drawing a line back 
to where you began) and fills in the middle.
  Fill Suppose your drawing contains a big area that's all the 
same color. For example, suppose you drew a big filled rectangle, 
circle, polygon, or blob. Here's how to change the color of that 
area.
  Click in the Color Palette, at the new color you want, so it 
becomes the foreground color. (The new color can be red, blue, 
black, white, or any other color you wish.)
  Click the Fill icon (which looks like a paint bucket).
  The mouse pointer turns into a paint bucket. Move the mouse 
pointer carefully, so the tip of the paint (spilling out of the 
bucket) is in the middle of the large area whose color you want 
to change. Then click.
  The entire area's color will change to the foreground color.
  If you make a mistake, click the Undo icon and try again.
  You can use that technique to change the color of any big area 
that's all the same color. For example, if you draw a big yellow 
sun, you can change the sun's color to orange.
  Here's how to start drawing a landscape. Clear the screen (by 
clicking the Clear icon). Then draw the horizon, as follows: by 
using the Squiggle icon, draw a horizontal black squiggle all the 
way across the screen. Make sure the squiggle goes all the way 
across the screen ___ from the screen's far left to the screen's 
far right ___ so that there are no gaps in the horizon, and so 
that it's impossible to travel from the sky (above the horizon) 
to the ground (below the horizon) without crossing the horizon.
  Then make the sky blue. To do that, click the blue part of the 
Color Palette icon, then click the Fill icon, then click in the 
middle of the sky. (If you're using Deluxe Paint 2 Enhanced in a 
2-color mode, pick black instead of blue and make a night scene.)
  The entire sky will turn blue (or black).
  If you made a mistake and forgot to make the horizon go all the 
way across the screen, the sky's blue paint will leak through the 
horizon and make the ground blue. Click the Undo icon and try 
again!
  To make the ground be desert brown or lawn green or 
fantasy-land purple, click your favorite ground color in the 
Color Palette, then click Fill, then click in the middle of the 
ground.
  Here's how to draw a face that's embarrassed. Clear the screen 
(by clicking the Clear icon). Begin using the Squiggle icon, draw 
the face's black outline (a circle with two bumps on it ___ for 
the ears). Make sure the face's bumpy circle is a complete circle 
and has no gaps. Make sure it's impossible to go from the middle 
of the face to the screen's edge without crossing the face's 
circle.
  Then make the face turn red. To do that, click the red part of 
the Color Palette icon, then click the Fill icon, then click in 
the middle of the face. The entire face will turn red.
  If you made a mistake and forgot to make the face's circle be 
complete, the face's red paint will bleed through the gap in the 
face's circle and make the rest of the screen be bloody. Yuk! 
Click the Undo icon and try again!
  Spray To vandalize your own drawing by using a can of spray 
paint, click the Spray icon (which looks like a can of spray 
paint and is also called the Airbrush icon). Then put the mouse 
pointer in the painting area, where you want to begin spraying, 
and drag!
  Text To put words in the middle of your picture, click the Text 
icon. Then click in the painting area, where you want the words 
to begin. Type the words.
                                         Grid To draw simple 
diagrams more easily, click the Grid icon before you draw. Then 
anytime you click or drag the mouse (except when drawing 
squiggles), the computer will automatically nudge the mouse 
pointer so that its X and Y coordinates are a multiple of 8.
                                         For example, try this 
experiment. Click the Grid icon. Draw a line (by using the Line 
icon). Now try to draw another line that starts at exactly the 
same point as the first line. Because of the grid, you don't have 
to bother putting the mouse pointer exactly where the first line 
began; just put the mouse pointer close to that point, and the 
computer will automatically nudge the mouse pointer so that its 
coordinates are a multiple of 8 ___ and exactly where the first 
line began.
                                         Magnify To magnify part 
of the screen temporarily, so you can see more clearly what 
you're drawing there, click the Magnify icon (which looks like a 
magnifying glass). Then click in the part of painting area you 
want to magnify.
                                         The screen splits into 
two parts. The left part of the screen shows the objects in their 
actual size; the right part of the screen shows the objects 
magnified.
                                         Go ahead: continue 
drawing! Whatever you draw will appear in the left part of the 
screen (actual size) and simultaneously in the right part of the 
screen (magnified).
                                         When you finish needing 
magnification, click the Magnify icon again. The screen will 
return to its usual, unmagnified state.
                                         Hand While looking at a 
magnified part of the screen, here's how to nudge the magnifying 
glass so you see a slightly different view.
                                         Click the Hand icon. 
(It's also called the Grabber icon.) Put the mouse pointer in the 
middle of the magnified view. Drag a short distance in the 
direction that you want to nudge the view.
                                         Symmetry To create 
perfect symmetry, click the Symmetry icon (which looks like a 
snowflake or the image seen through a kaleidoscope). Then move 
the mouse pointer near the center of the painting area. You'll 
see the mouse pointer and 11 clones of it ___ 12 pointers 
altogether, arranged in a circle.
                                         Go ahead: continue 
drawing! Whatever you draw will be duplicated 11 extra times, so 
you'll see 12 copies of your drawing. The 12 copies are arranged 
in a circle and rotated, and 6 of those copies are mirror images 
(flipped backwards). Groovy!
                                         When you finish 
symmetric drawing, click the Symmetry icon again. Then you'll 
have just one mouse pointer, instead of 12.
           Pop out a menu
  You can make the screen display extra icons. Here's how.
  Zigzag Try this experiment. Point at the Line icon, then hold 
down the mouse's left button awhile. A new menu pops out onto the 
screen. (It's called a pop-out menu). The menu shows two icons. 
One of them is a copy of the Line icon. The other is the Zigzag 
icon: it's a line with a bend in it. To use the Zigzag icon, drag 
to it.
  Here's how to draw a zigzag (try it!). Drag to the Zigzag icon 
(which pops out of the Line icon). Then click in the painting 
area, where you want the zigzag to begin. Click where you want 
the zigzag's first bend. Click where you want the zigzag's second 
bend. Click at each additional bend. Click where you want the 
zigzag to end. Then press the SPACE bar. (If the zigzag's ending 
point is the same as where the zigzag began, pressing the SPACE 
bar is optional.)
  The Zigzag icon is also called the ``Connected Lines'' icon or 
``Polyline'' icon.
  After you've used the Zigzag icon, that icon stays on the 
screen, where the Line icon used to be.
  If you ever want to draw a simple line again, make the Line 
icon reappear. Here's how. Point at the Zigzag icon. Hold down 
the mouse's left button. You'll see the pop-out menu again. Drag 
to the pop-out menu's Line icon.
  Practice drawing zigzags, then simple lines, then zigzags 
again. When you feel comfortable, explore the following icons, 
which are more advanced. . . . 
  Zigzag arcs To draw a zigzag made of a series of arcs instead 
of lines, drag to the Zigzag Arcs icon, which pops out of the Arc 
icon. Then point in the painting area, where you want the first 
arc to begin, and drag to where you want that arc to end. Lift 
your finger off the mouse's button. Move the mouse until that arc 
has the curvature you wish, then click.
  Click where you want the second arc to end, and click where you 
want that second arc to curve. Click where you want the third arc 
to end, and click where you want the third arc to curve. Do the 
other arcs.
  When you finish the last arc, press the SPACE bar.
  The Zigzag Arcs icon is also called the ``Connected curves'' 
icon or ``Polycurve'' icon.
  Extended color palette If you're using Deluxe Paint Animation 
(or Deluxe Paint 2 Enhanced in a 256-color mode), try this trick. 
In the Color Palette icon, point at one of the colors, and hold 
down the mouse's left button awhile. You'll see a pop-out menu 
displaying all 256 colors simultaneously. Drag to the color you 
want. It becomes the foreground color.
  If you're using Deluxe Paint 2 Enhanced in a 16-color mode, try 
this similar trick instead. In the Color Palette icon, point at 
your favorite color, and hold down the mouse's left button 
awhile. You'll see a pop-out menu that displays 16 modifications 
of that color. (The computer creates the modifications by adding 
tiny polka dots made of the other colors. The modifications made 
by polka dots are called dithers.) Drag to whichever dither you 
like. That dither becomes the foreground color.
                                         Modified rectangles 
Point at the Filled Rectangle icon, and hold down the mouse's 
left button.
                                         You'll see four pop-out 
icons. One of them is a copy of the Filled Rectangle icon. 
Another (Filled Square) acts like the Filled Rectangle icon but 
always produces a perfect square. The other two icons (Unfilled 
Rectangle and Unfilled Square) let you draw an outline shape 
whose middle is not filled in.
                                         Modified circles Point 
at the Filled Circle icon, and hold down the mouse's left button.
                                         You'll see six pop-out 
icons. One of them is a copy of the Filled Circle icon. The other 
pop-out icons are Filled Ellipse, Filled Rotated Ellipse, 
Unfilled Circle, Unfilled Ellipse, and Unfilled Rotated Ellipse.
                                         To draw a filled ellipse 
(oval), choose the Filled Ellipse icon. Then in the painting 
area, imagine a rectangle just big enough to contain the ellipse 
you want. (That's called the bounding rectangle.) Point at that 
rectangle's top left corner, and drag to the opposite corner. The 
ellipse will appear.
                                         To draw a filled rotated 
ellipse, choose the Filled Rotated Ellipse icon. Then click in 
the painting area, where you want the ellipse's center to be. 
Move the mouse until the ellipse is as fat and tall as you wish. 
Then drag in a circular motion, until the ellipse is rotated to 
the angle you wish.
                                         Unfilled polygon The 
Unfilled Polygon icon pops out of the Filled Polygon icon.
                                         Modified squiggles Point 
at the Squiggle icon, which looks like a paintbrush that's 
drawing a squiggle. Hold down the mouse's left button. You'll see 
three pop-out icons.
                                         One of them is a copy of 
the Squiggle icon.
                                         Another popped-out icon 
(Dotted Squiggle) acts like the Squiggle icon but makes the 
squiggle be a series of dots instead of a continuous curve. If 
you want the dots to be far apart, drag the mouse fast while 
drawing the dotted squiggle. That icon is also called the 
Discontinuous Freehand Brush icon.
                                         The other popped-out 
icon (Stopped Squiggle) produces just a single dot instead of a 
complete squiggle. Since it stamps just one dot onto your screen, 
it's also called the Single-Stamp Freehand Brush icon.
                                         Magnification level When 
you use the Magnify icon, it normally magnifies objects by a 
factor of 4, so that each object appears 4 times as wide and 4 
times as tall. That's called a magnification level of 4x.
                                         To choose a different 
magnification level, point at the Magnify icon and hold down the 
mouse's left button. You'll see a pop-out menu that offers these 
magnification levels: 2x, 3x, 4x, 6x, 8x, 12x, and 16x. Drag to 
the magnification level you want.
           Choose a brush
  To draw without a computer, you can buy a collection of 
paintbrushes. To draw a thick line, use a thick brush. To draw a 
thin line, use a brush that's tiny and fine. To create a weird 
texture, paint with a toothbrush. To create a big weird texture, 
paint with a hairbrush. To create a gigantic weird texture, get 
together with your friends, undress, cover yourselves with paint, 
and roll around on a large sheet of canvas. (That's called 
Technicolor mud wrestling. It's a quick, fun way to create an 
abstract pop mural. The mural makes a great conversation piece 
when you match the shapes on it with the various people and their 
parts.)
  Your computer lets you paint on the screen by using all kinds 
of brushes. You can even invent your own brush, having any shape 
you like!
  Here's how to pick a brush.
  Built-in brushes Point at the One-Dot Brush icon, and hold down 
the mouse's left button.
  You'll see 18 brush shapes. Some of them are round brushes. 
Some are square. Some have multiple tufts (like a tiny 
toothbrush, or like a paintbrush whose bristles have been 
purposely frayed apart). Some are chisel-pointed (like a 
miniature ax, for calligraphy and Japanese effects). They're 
called the 18 built-in brushes.
  Drag to whichever built-in brush interests you, and try it! The 
computer will use that brush to draw all shapes (squiggles, 
lines, arcs, etc.), until you switch to a different brush.
  Custom brushes Here's how to invent your own brush.
  First, decide what shape you want the brush to produce when you 
tap the brush onto paper. Do you want the resulting shape to be a 
tiny dot, or a circle, or a square, or an irregular blob, or blob 
that's the same shape as a ear, or a blob that looks like Bart 
Simpson's hair, or some other weird shape?
  Draw that shape in the painting area. (For example, if you want 
the brush's blob to look like Bart Simpson's hair, draw a picture 
of Bart Simpson's hair.) When drawing that shape, use your 
favorite colors!
  To make that shape become your brush, click the Brush Pickup 
icon. Then draw a rectangle around the shape: point where you 
want the rectangle's top left corner, and drag to where you want 
the rectange's opposite corner. When you lift your finger off the 
mouse's button, the shape becomes your new brush. Its colors 
become the new colors you'll be drawing in.
  The computer will automatically click the Dotted Squiggle icon 
for you. Go have fun! Drag the mouse wherever you wish! As you 
drag, you'll be drawing dotted squiggles by using your new brush 
and colors.
  The brush you invented is called a custom brush. It will be 
your brush until you invent a different custom brush or switch 
back to one of the 18 built-in brushes (by clicking the One-Dot 
Brush icon).


           EXOTIC GRAPHICS
  There's more to painting than just Deluxe Paint!

        Mac Paint's children
  Although Deluxe Paint is a good painting program, it wasn't the 
first. The first popular painting program ever invented was Mac 
Paint. It was invented in 1984 ___ the year before Deluxe Paint. 
It was invented by Bill Atkinson at Apple Computer Ince. To use 
it, you had to buy a Mac. At first, it was included free with the 
Mac. Later, Apple priced it at $149.
  In 1986, Ann Arbor Software published an improved Mac Paint 
called Full Paint. A few months later, at the end of 1986, 
Silicon Beach published an even fancier program, called Super 
Paint. They understand all Mac Paint's commands, plus more. 
Discount dealers sell Super Paint 1.1 for $79 and Super Paint 2 
for $109.
  In 1987, Apple created a spin-off company, Claris, to publish 
Mac Paint. Claris developed Mac Paint 2, which is fancier than 
the original Mac Paint but not as fancy as Full Paint, Super 
Paint, or Deluxe Paint.

              Clip art
  Some artists sell little cartoons that you can insert into your 
own masterpiece. Those cartoons are called clip art. You can buy 
a disk containing hundreds of little cartoons, stick that disk 
into your computer, and insert your favorite cartoons into your 
Deluxe Paint masterpiece.
  By using Deluxe Paint commands, you can modify the cartoons to 
suit your own taste. For example, you can make a cartoon larger 
or smaller, or change the expression on the person's face, or 
change the writing in the bubble that comes out of the person's 
mouth.
  Computer dealers sell dozens of disks full of such cartoons. 
Copying and editing those cartoons is much faster than creating 
your own art from scratch.

            Thunder Scan
  You can attach the computer to a video camera, and feed the 
video picture directly into the computer, so the computer can 
manipulate the picture.
  The cheapest way to do that is to buy a teeny-weeny video 
camera called the Thunder Scan. It comes in a cartridge. To use 
it, buy a Mac Imagewriter printer, remove the printer's ribbon 
cartridge, and insert the Thunder Scan cartridge instead. Then 
turn on the printer; but instead of inserting blank paper, insert 
any page containing a photo. The printer tries to move the ribbon 
back and forth, to print; but since the ribbon's been replaced by 
the Thunder Scan camera, the printer moves the camera instead; so 
the camera moves back and forth over the entire photo, scans the 
photo, and feeds it through a wire to the Mac's RAM, which 
displays the photo on the Mac's screen. Then you can copy the 
photo to the disk, and edit the picture by using Mac Paint.
  Thunder Scan was invented by Andy Hertzfeld, who also helped 
invent the Mac. Thunder Scan lists for $249, but discount dealers 
(such as Mac Connection) sell it for just $199.
                                                        CAD
                                         To design a building (or 
machine), you must create a blueprint. Making the computer create 
a blueprint is called computer-aided drafting (or computer-aided 
design or CAD). If those blueprints are fed to computerized 
machines that manufacture the parts for the building, the whole 
process is called computer-aided design & computer-aided 
manufacturing (CAD/CAM).
                                         Many architects and 
engineers use CAD programs. The CAD programs resemble Deluxe 
Paint but have several advantages. . . . 
                                         The CAD programs can do 
math. They can look at your diagrams, compute all the 
measurements (lengths, surface areas, and volumes), and write 
those measurements on the blueprints.
                                         The CAD programs can do 
advanced geometry. For example, they can draw a circle, even if 
you don't tell the center and radius. Just say three points that 
you want the circle to touch! The CAD programs will figure out 
which circle goes through those three points and will draw it.
                                         After you've drawn an 
object, the CAD programs can rotate it and show you the views 
from different angles, in the form of blueprints or as artistic 
perspective drawings.
                                         The CAD programs let you 
name the parts of your object and move the parts around. If one 
part covers another part and hides it, the CAD programs remember 
that the hidden part is still there, so that the hidden part will 
automatically reappear if you ever more the other part out of the 
way.
                                         Although CAD programs 
are excellent for drawing and analyzing straight lines, circles, 
and ovals, they're not good at handling artistic squiggles. So if 
you're an artist who likes to draw wild squiggles, do not get a 
CAD program: instead, stick with Deluxe Paint. CAD programs are 
strictly for architects, engineers, and other folks who do 
technical drafting.
                                         Traditional top-notch 
CAD programs require you to sit at a fancy screen (called a 
graphics workstation) attached to an expensive computer costing 
over $50,000. Newer CAD programs work on microcomputers and are 
almost as fancy.
                                         The fanciest CAD program 
for microcomputers is Autocad. The newest version of Autocad 
lists for $3500; it requires an IBM AT (or AT clone) and a math 
coprocessor chip (which helps the computer handle decimals 
quickly). A stripped-down version, called Autocad Lite, sells for 
about $400. A fun version, called Autosketch, lists for just $80 
and runs on any IBM clone.
                                         Autocad's main 
competitor is Cadkey, which has more commands for 3-dimensional 
drawing but fewer commands for 2-dimensional drawing. It lists 
for $3195.
                                         The first CAD program 
for the Mac was Mac Draw. For elementary CAD applications, you 
can get by with Super Paint, which includes some of the commands 
of Mac Draw plus all the commands of Mac Paint. Better CAD 
programs for the Mac are being developed.
          Business graphics
  Business executives like to turn tables of numbers into pie 
charts and bar charts. The most popular way to produce those 
charts is to use a spreadsheet program (such as Lotus 1-2-3), 
which lets you type a table of numbers and then say ``Graph''.
  Lotus 1-2-3 produces just a few types of graphs, and its graphs 
look crude. To create graphs that are fancier and prettier, buy a 
fancier spreadsheet program (such as Microsoft Excel) or a 
presentation-graphics program (such as Microsoft Powerpoint or 
Lotus Freelance or Harvard Graphics). Those presentation-graphics 
programs are especially good for preparing slide shows and 
overhead transparencies.


        CLASSIC COMPUTER ART
  During the 1960's, many creative ideas were generated about how 
computers would someday create their own weird art, using a wild 
combination of formulas and random numbers, and unshackled by the 
bounds of human culture.
  Here's how to make the computer produce wild art, by using the 
wonderful classic tricks invented in the 1960's and 1970's. . . . 

             Gray levels
  You can express every black-and-white photograph as a table of 
numbers. Each number in the table represents the darkness of a 
different point ___ the higher the number, the darker the point. 
The ``darkness numbers'' are called gray levels. To feed a 
picture into the computer, type in the table of gray levels. Or 
aim a special camera at the object you want pictured; the camera 
system will automatically compute the gray levels and send them 
to the computer via a wire.
  You can program the computer to change the gray levels in any 
weird way you wish, and draw the result. In the 1960's, the 
Computer Technique Group of Japan did this to an ordinary 
photograph of John Kennedy:
Shot Kennedy        Diffused Kennedy
                    Kennedy in a Dog

                                         Here's what the group 
did to a photograph of Marilyn Monroe:
                                                 Monroe in the Net
                                         Csuri & Shaffer fed the 
computer a realistic line drawing of an old man; here's what came 
out:
                                              Random Light and Shadow

  I did this with the help of a computer:
         Pin-Up
  The Pin-Up has these specifications. . . . 
scene: a scantily clad woman sitting on a stool

4 gray levels

4 symbols (1 for each gray level: a blank, a period, an asterisk, 
and a dollar sign)

1537 symbols altogether (53 rows x 29 columns)
In the specification, the numbers are small, yet the picture is 
clear. To obtain the clarity, I did non-computerized finagling.
                             At Bell Telephone Laboratories, 
Knowlton & Harmon produced a picture with much larger 
specifications. . . . 
scene: two sea gulls flying in the clouds
16 gray levels
141 symbols (each gray level has several symbols; the computer 
chooses among them at random)
11616 symbols altogether (88 rows x 132 columns)
Instead of using blanks, periods, asterisks, and $, they used 
cats, battleships, swastikas, and other weird shapes. Here are 
the 141, listed from lightest to darkest, with some repetitions:
The picture is several feet long. Seen from a distance, it looks 
like this:
                                                 Gulls

Here's a close-up view of part of one of the gull's wings:
  If you don't like sea gulls, how about Mona Lisa?

                                         In 1971, Michael Hord 
made the computer turn photographs into artistic sketches. Here's 
what the computer did to a photograph of his boss, and to a 
photograph of a colleague's girlfriend:
                                                       Boss
                                                       Woman
To draw each sketch, the computer's camera scanned the original 
photograph and found the points where the photograph changed 
dramatically from light to dark. Then, on a sheet of paper, it 
plotted those points; and through each of those points, it drew a 
short line perpendicular to the direction in which the original 
photograph darkened.
  More precisely, here's what the computer did. . . . It looked 
at four adjacent points on the original photograph:
A B
C D
It computed the darkness of each of those points. Then it 
computed the ``darkening in the X direction'', defined as:
(darkness at B) + (darkness at D) - (darkness at A) - (darkness 
at C)
Then it computed the ``darkening in the Y direction'', defined 
as:
(darkness at A) + (darkness at B) - (darkness at C) - (darkness 
at D)
Then it computed the ``overall darkening'', defined as:
(darkening in the X direction) + (darkening in the Y direction)
If the overall darkening there turned out to be large, the 
computer sketched a short line, in the vicinity of the points 
ABCD, and perpendicular to the direction of darkening. More 
precisely, the line's length was 1, and the line's slope was:
  the darkening in the X direction
-
  the darkening in the Y direction

               Morphs
  Here's how to make an L slowly become a V. Notice that the 
letters L and V are both made by connecting three points:
Let 1" be the point halfway between 1 and 1'; let 2" be halfway 
between 2 and 2'; and let 3" be halfway between 3 and 3'. Then 
1", 2", and 3" form a shape that's halfway between an L and a V:
The process can be extended further:
  Turning one shape into another (such as turning an L into a V) 
is called a metamorphosis or morphing. The intermediate shapes 
(that are between the L and the V) are called the morphs.
  Using that method, the Computer Technique Group of Japan 
gradually turned a running man into a Coke bottle, and then into 
Africa:
       Running Cola is Africa

The group turned this head into a square:
                                                Return to a Square
The head on the left returns to a square by using arithmetic 
progression: the lines are equally spaced. The one on the right 
uses geometric progression instead: the lines are close together 
near the inside square, but further apart as they expand outward.
                                         Csuri & Shaffer exploded 
a hummingbird:
                                                  Chaos to Order
The hummingbird at the far right was obtained from the one at the 
far left, by moving each line a random distance and in a random 
direction (between 45 and -45).
                                         Computers can make 
movies. The best movie ever made by a computer is called Hunger 
(or La Faim). It was made under the auspices of the Canadian Film 
Board. It's a 10-minute cartoon, in color, with music; but it 
goes far beyond anything ever done by Walt Disney. It uses the 
same technique as Running Cola is Africa: it shows objects 
turning into other objects.
                                         It begins by showing a 
harried, thin executive at his desk, which has two phones. One of 
the phones rings. He answers it. While he's talking on that 
phone, his other phone rings. To talk on both phones 
simultaneously, his body splits in two. (How does a single body 
become two bodies? By using the same technique as turning a 
running man into a coke bottle.)
                                         On the other side of his 
desk is an armchair, which turns into a secretary, whose head 
turns into a clock saying 5PM, which tells the executive to go 
home. So he stretches his arms in front of him, and becomes his 
car: his hands become the headlights, his arms become the front 
fenders, his face becomes the windshield. You have to see it to 
believe it.
                                         He drives to a 
restaurant and gets the waitress, who turns into an ice-cream 
cone. Then he eats her.
                                         As the film progresses, 
he becomes increasingly fat, lustful, slothful, and miserable. In 
the end, he falls into hell, where he's encircled by all the poor 
starving naked children of the world, who eat his flesh. then the 
film ends. (Don't see it before eating dinner!)
                                         It combines computer art 
and left-wing humanitarian politics, to create an unforgettable 
message.
  Now morphing is being applied to color photographs and video 
images. For example, Hollywood movies use morphing to show a 
person gradually turning into a monster; environmentalists use 
morphing to show a human baby gradually turning into a spotted 
owl; and portrait photographers who have gone high-tech use 
morphing to show you gradually turning into the person you admire 
most (such as your movie idol or your lover).

        Order versus disorder
  Computer artists are starting to believe that art is a tension 
between order and disorder. Too much order, or too much disorder, 
will bore you. For example, in Chaos to Order, the hummingbird on 
the left is too orderly to be art. The hummingbird on the right 
is more interesting.
  Consider Gulls. Seen from a distance, it's an orderly picture 
of gulls. Seen up close, it's an orderly picture of a cat or 
battleship or swastika. But from a middling distance, it looks 
like disorderly wallpaper: the symbols repeat, but not in any 
obvious cycle. That element of disorder is what makes the picture 
interesting.
  At first glance, Pin-Up is just a disorderly array of periods, 
asterisks, and dollar signs. At second glance, you see order: a 
girl. Art is the formation of order from disorder.
  A first glance at Monroe in the Net shows order: a piece of 
graph paper. A second glance shows disorder: some of the graph's 
lines are inexplicably bent. A third glance shows order: Marilyn 
Monroe's face pops out at you. Her orderly face is formed from 
the disorder of bent lines.
  Return to a Square uses arithmetic progression and geometric 
progression to create an over-all sense of order, but the basic 
elements are disorderly: a head that's bumpy, and a panorama of 
weird shapes that lie uncomfortably between being heads and 
squares but are neither.
  Many programs create disorder by random numbers. Chaos to Order 
uses random numbers to explode the hummingbird. Gulls uses random 
numbers to help choose among the 141 symbols.
  An amazing example of random numbers is this picture by Julesz 
& Bosche:
To your eyes, the picture seems quite ordered. Actually, it's 
quite disordered. One pie-shaped eighth of it is entirely random; 
the other seven eighths are copies of it. The copying is the only 
element of order, but very powerful. Try this experiment: cover 
seven-eighths of the picture. You'll see that the remaining 
eighth is totally disordered, hence boring.
                                         That program imitates a 
child's kaleidoscope. Do you remember your childhood days, when 
you played with your kaleidoscope? It was a cardboard 
``telescope'' that contained a disorganized pile of colored glass 
and stones, plus a series of mirrors that produced eight-way 
symmetry, so that what you saw resembled a giant multicolored 
snowflake. The program by Julesz & Bosche uses the same 
technique, computerized. Hundreds of programmers have imitated 
Julesz & Bosche, so that today you can buy kaleidoscope programs 
for your Apple, Radio Shack, etc. Or try writing your own!
                                         Take this test:
One of those is a famous painting (Composition with Lines, by 
Piet Mondrian, 1917). The other was done by a computer 
(programmed by A. Michael Noll in 1965). Which one was done by 
the computer? Which one do you like best?
                                         The solution is on the 
next page, but don't peek until you've answered!
  The computer did the top one.
  The programmer surveyed 100 people. Most of them (59) thought 
the computer did the bottom one. Most of them (72) preferred the 
top one ___ the one that was actually done by the computer.
  The test shows that people can't distinguish computer art from 
human art, and that the computer's art is more pleasing that the 
art of a famous painter.
  The computer's version is more disordered than Mondrian's. The 
computer created the disorder by using random numbers. The survey 
shows that most people like disorder: Mondrian's work is too 
ordered. It also shows that most people mistakenly think the 
``computer'' means ``order''.

              Envelopes
  Try this experiment. On a piece of paper, put two dots, like 
this:
The dots represent little insects, or ``bugs''. The first bug is 
looking at the second bug. Draw the first bug's line of sight:
Make the first bug take a step toward the second bug:
Make the second bug run away, in any direction:
  Now repeat the entire process. Again, bug 1 looks at bug 2; 
draw its line of sight:
Bug 1 moves toward bug 2:
Bug 2 keeps running away:
  If you repeat the process many times, you get this:
The ``motion of bug 1'' looks like a curve. (In fact, it's a 
parabola.) The ``curve'' is composed of many straight lines ___ 
the lines of sight. That's how to draw a fancy curve by using 
straight lines.
  Each straight line is called a tangent of the curve. The entire 
collection of straight lines is called the curve's envelope. 
Creating a curve, by drawing the curve's envelope, is called 
stitching the curve ___ because the lines of sight act as 
threads, to produce a beautiful curved fabric.
                                         You can program the 
computer to draw those straight lines. That's how to make the 
computer draw a fancy curve ___ even if you know nothing about 
``equations of curves''.
                                         To get a curve that's 
more interesting, try these experiments:
What if bug 2 doesn't walk in a straight line? What if bug 2 
walks in a curve instead?

What if bug 1 goes slower than bug 2, and takes smaller steps?

What if the bugs accelerate, or slow down?

What if there are three bugs? What if bug 1 chases bug 2, while 
bug 2 chases bug 3, while bug 3 chases bug 1?

What if there are many bugs, all chasing each other, and their 
starting positions are random?

What if there are just two bugs, but the bugs are Volkswagens, 
which must drive on a highway having nasty curves? Show the bugs 
driving on the curved highway. (Their lines of sight are still 
straight; but instead of moving along their lines of sight, they 
must move along the curve that represents the highway.)
What if each bug has its own highway, and all the bugs stare at 
each other?
                                         Here are some elaborate 
examples. . . . 
                                         Four bugs chasing each 
other:

  The next example, called Compelling, appeared in the famous 
book and movie, The Dot and the Line. (Norton Juster made it by 
modifying art that had appeared in Scripta Mathematica.) It 
resembles the example above, but makes the 4 bugs start as a 
rectangle (instead of a square), and makes the bug in the upper 
left corner chase the bug in the opposite corner (although 
looking at a nearby bug instead).
  Enigmatic (from The Dot and the Line) makes 3 bugs chase each 
other, and a fourth bug stay motionless in the center:
  I invented Kite, which has 8 bugs chasing each other:
I also invented Sails, which has 14 bugs chasing each other:
                                         Elliptic Motion (by my 
student Toby D'Oench) has 3 bugs staring at each other, as they 
travel on 3 elliptical highways:
                                         Archimedean Spiral (by 
Norton Starr) has bugs on circles. The bugs stare at each other 
but don't move:
              Fractals
  A fractal is an infinitely bumpy line. Here's how to draw one.
  Start by drawing a 1-inch line segment:
  In the middle of that segment, put a bump and dip, like this:
Altogether, that bent path is 2 inches long. In other words, if 
the path were made of string, and you stretched the string until 
it was straight, the string would be 2 inches long. That's twice 
as long as the 1-inch line segment we started with. So here's the 
rule: putting a bump and dip in a path makes the path twice as 
long.
  That bent path consists of seven segments. Put a bump and a dip 
in the middle of each segment, like this:
Altogether, those bumps and dips make the path twice as long 
again, so now the path is 4 inches long.
  Again, put a bump and dip in the middle of each segment, so you 
get this:
Again the path's length has been doubled, so now the path is 8 
inches long.
  If you again put a bump and dip in the middle of each segment, 
the path's length doubles again, so the path becomes 16 inches 
long. If you repeat the procedure again, the path reaches 32 
inches.
  If you repeat that procedure infinitely often, you'll develop a 
path that's infinitely wiggly and infinitely long. That path is 
longer than any finite line segment. It's longer than any finite 
1-dimensional object. But it still isn't a 2-dimensional object, 
since it isn't an ``enclosed area''. Since it's bigger than 
1-dimensional but isn't quite 2-dimensional, it's called 
1-dimensional. Since 1 contains a fraction, it's called 
fractional-dimensional or, more briefly, fractal.
  Look out your window at the horizon. What do you see? The 
horizon is a horizontal line with bumps (which represent hills 
and buildings and other objects). But on each hill, you see tiny 
bumps, which are trees; and on each tree, you see even tinier 
bumps, which are leaves; and on each leaf, you see even tinier 
bumps, which are the various parts of the leaf; and each part of 
the leaf is made of even smaller bumps (molecules), which have 
even smaller bumps (atoms), which have even smaller bumps 
(subatomic particles). Yes, the horizon is an infinitely bumpy 
line, a fractal!
  You can buy software that creates fractals. Computer artists 
use fractal software to draw horizons, landscapes, and other 
bumpy biological objects. For example, they used fractal software 
to create landscapes for the Star Wars movies. You can also use 
fractals to draw a bumpy face that has zillions of zits.
                                         Now you understand the 
computer artist's philosophy of life: ``Life is a lot of lumps.''

                                                    What's art?
                                         To create art, write a 
weird program whose consequences you don't fully understand, tell 
the computer to obey it, and look at the computer's drawing. If 
the drawing looks nice, keep it and call it ``art'' ___ even if 
the drawing wasn't what you expected. Maybe it resulted from an 
error, but so what? Anything interesting is art.
                                         If the drawing ``has 
potential'' but isn't totally satisfying, change a few lines of 
the program and see what happens ___ or run the program again 
unchanged and hope the random numbers will fall differently. The 
last thing to invent is the title. Whatever the drawing reminds 
you of becomes the title.
                                         For example, that's how 
I produced Kite and Sails. I did not say to myself, ``I want to 
draw a kite and sails''. I just let the computer pick random 
starting points for the bugs and watched what happened. I said to 
myself, ``Gee whiz, those drawings remind me of a kite and 
sails.'' So I named them Kite and Sails, and pretended that I 
chose those shapes on purpose.
                                         That method may seem a 
long way from DaVinci, but it's how most computer art gets 
created. The rationale is: don't overplan. . . . let the computer 
``do its own thing''; it will give you art that escapes from the 
bounds of human culture and so expands your horizons!

                                                   Modern style
                                         Computer art has 
changed. The classic style ___ which you've been looking at ___ 
consists of hundreds of thin lines in mathematical patterns, 
drawn on paper and with little regard for color. The modern style 
uses big blobs and streaks of color, flashed on a T.V. tube or 
film, which is then photographed.

                                                  Uncreative art
                                         You've seen that 
computers can create their own weird art by using a wild 
combination of formulas and random numbers, unshackled by the 
bounds of human culture.
                                         Today, programs such as 
Deluxe Paint let people use computers to create art easily and 
cheaply. Unfortunately, the typical person who buys a graphics 
program uses it to create the same kind of junk art that would be 
created by hand ___ just faster and more precisely. That's the 
problem with computers: they make the production of mediocrity 
even easier and more glitzy.

             3-D DRAWING
  The computer drew these three-dimensional surfaces:
             Three Peaks
            by John Szabo
                 Dip
  Those were done for the sake of art. This was done for the sake 
of science:
   Population Density in the U.S.
by the Harvard University Mapping Service
  The hardest part about three-dimensional drawing is figuring 
out which lines the computer should not show, because they're 
hidden behind other surfaces.

             Coordinates
  Try this experiment. Put your finger on the bridge of your nose 
(between your eyes). Now move your finger 2 inches to the right 
(so that your finger is close to your right eye). Then move your 
finger 3 inches up (so that your finger is near the upper right 
corner of your forehead). From there, move your finger 8 inches 
forward (so that your finger is 8 inches in front of your 
forehead).
  Your finger's current position is called (2,3,8), because you 
reached it by moving 2 inches right, then 3 inches up, then 8 
inches forward. The 2 is called the X coordinate; the 3 is called 
the Y coordinate; the 8 is called the Z coordinate.
  You can reach any point in the universe by the same method! 
Start at the bridge of your nose, and get to the point by moving 
right (or left), then up (or down), then forward (or back).
                                         The distance you move to 
the right is called the X coordinate (if you move to the left 
instead, the X coordinate is a negative number). The distance you 
move up is called the Y coordinate (if you move down instead, the 
Y coordinate is a negative number). The distance you move forward 
is called the Z coordinate (if you move back instead, the Z 
coordinate is a negative number).

                                            Projecting the coordinates
                                         To draw a picture of a 
three-dimensional object, put the object in front of you, and 
then follow these instructions. . . . Pick a point on the object. 
(If the object has corners, pick one of the corners.) Figure out 
that point's X, Y, and Z coordinates (by putting your finger on 
the bridge of your nose and then seeing how far you must move 
your finger right, up, and forward to reach the object).
                                         Then compute the point's 
projected X coordinate (which is X/Z) and the point's projected Y 
coordinate (which is Y/Z). For example, if X is 2 and Y is 3 and 
Z is 8, the projected X coordinate is 2/8 (which is .25) and the 
projected Y coordinate is 3/8 (which is .375). On graph paper, 
plot the projected X coordinate and the projected Y coordinate, 
like this:
Then plot the point:
Go through the same procedure for every point on the object (or 
at least for the corners). Connect the dots and ___ presto! ___ 
you have a three-dimensional picture of the object! And the 
picture is mathematically accurate! It's what artists call a 
``true perspective drawing''.
                                         To make the picture look 
traditionally beautiful, place the object slightly to the left of 
you and slightly below your eye level, so that all the X and Y 
coordinates become negative.

                                             Computerizing the process
                                         You can program the 
computer so that if you input a point's X coordinate, Y 
coordinate, and Z coordinate, the computer will calculate the 
projected X coordinate (from dividing X by Z) and the projected Y 
coordinate (from dividing Y by Z) and plot the point on the 
computer's screen (by using high-resolution graphics).
                                         The easiest way to draw 
three-dimensional pictures is to buy a special three-dimensional 
arm that attaches to an Apple computer. To draw a picture of an 
object, move the mechanical arm until the arm's finger touches 
the object. Immediately the arm's software computes the X 
coordinate, Y coordinate, and Z coordinate of the touched point; 
you don't need a ruler! It also computes the projected X 
coordinate and the projected Y coordinate and plots the points on 
your television. If you have a graphics printer, the software 
also plots the point on your printer's paper.