A Mandelbrot set plotter for the TI-82. Runs in about 1 hour.
ZOOMing is possible. Demonstrates 'End' problems.


 
    TOCCATA is Freeware
    Commercial Distribution Restricted
    Copyright (C) 1994 by Mikael Bonnier, Lund, Sweden.
 
1. System and Memory Requirements
This program is for the TI-82. It consists of one main program,
that uses 127 bytes. It requires an additional 60 bytes for data
to execute.
 
2. Installation
If you have TI-GRAPH LINK UUDecode this file, and send the resulting
TOCCATA.82P program to the calculator. If you don't have the 
link you will have to enter the ASCII82P listing below. 
 
4. User Instructions
This is a small Mandelbrot set plotting program. The Mandelbrot set M,
is the set of points c, in the complex plane so that z^2+c -> z doesn't
go to infinity when iterated (z=0 initially).
 
Since the TI-82 doesn't have complex arithmetic I have simplified
    (U+iV)^2+(X+iY) -> U+iV,
and separated the real and imaginary parts.
 
Suggested WINDOW settings (you can use ZOOM and rerun the program
afterwards) is:
    Xmin=-4, Xmax=4, Ymin=-4*62/94, Ymax=4*62/94.
With these settings it takes about one hour to run the program.
 
This program alters N,T,U,V.
 
5. Program Comments
* The 'Vertical' instruction makes TOCCATA interesting to watch.
* It is very difficult to use 'For(' for the inner loop since jumping
over an 'End' causes a problem - the next encountered 'End' would 
jump back to just after the 'For('. If TI should fix this, this
program will not work as written. Notice this program has three 'End's
but only two 'For's
* The temporary variable 'T' is necessary.
* 'If U\^2\+V\^2\>4', means that for this c value z will go to 
infinity, this was proved by Pierre Fatou, 1905.
* 'Pt-Off(X,Y)', the points not belonging to the set are turned off.
 
 
Suggestions, bug and bad-English-in-doc reports are always welcome to:
                    Mikael Bonnier
                    Osten Undens gata 88
                    S-227 62  LUND
                    SWEDEN
                             
Or use my internet address:
                    mikaelb@loglady.df.lth.se
 
// Mikael Bonnier
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