A Mandelbrot set plotter for the TI-82. Runs in about 1 hour.
ZOOMing is possible. Demonstrates 'End' problems.
----begin documentation----
TOCCATA v1.0 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
SE-227 62 LUND
SWEDEN
Or use my internet addresses:
mikael.bonnier@gmail.com
http://www.df.lth.se.orbin.se/~mikaelb/
// Mikael Bonnier
/////////////////////////////////////////////////////////////////////
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----begin ASCII----
\START82\
\COMMENT=1994 Mikael Bonnier,mikael.bonnier@gmail.com
\NAME=TOCCATA
\FILE=TOCCATA.82P
FnOff :AxesOff
PlotsOff
ClrDraw
DispGraph
For(X,Xmin,Xmax,\Delta-x\)
Vertical X
For(Y,Ymin,Ymax,\Delta-y\)
0\->\U
0\->\V
1\->\N
Lbl N
U\^2\-V\^2\+X\->\T
2UV+Y\->\V
T\->\U
If U\^2\+V\^2\>4
Goto X
IS>(N,100)
Goto N
End
Lbl X
Pt-Off(X,Y)
End
End
\STOP82\
----end ASCII----
----begin UUE----
begin 644 TOCCATA.82P
M*BI423@R*BH:"@`Q.3DT($UI:V%E;"!";VYN:65R+&UI:V%E;&)`9&8N;'1H
M+G-E``````"$``L`=0`%5$]#0T%400!U`',`ESY^"3_J/X4_WS_36"MC"BMC
M"RMC)A$_G5@_TUDK8PPK8PTK8R<1/S`$53\P!%8_,01./]9./U4-<58-<%@$
M5#\R559P6016/U0$53_.50UP5@UL-#_76#_:3BLQ,#`1/]=./]0_UE@_GU@K
)61$_U#_4/]LG
`
end
----end UUE----