Sierpinski square TI84+CE
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Here are two programs I created for my TI84+CE that draws a Sierpinski square (well, 2/3rds of one anyways). The first one draws a small square, creating a larger square as it goes. The second one draws pixels at different screen positions filling in the pattern as it runs. Because of the screen size, I can only draw 2/3rds of the square at the size I’m drawing. It takes 6min, 30seconds to complete the drawing. There are several FOR loops, but at some point I might try to make it recursive on my calculator. I have it recursive on my iPad which draws the full square instantly. I also have code on my iPad that draws an 81x81x81 Sierpenski cube in about 2 seconds.

Just a note, there are 2 programs listed. They should be loaded separately.

I changed the 81 value for loops to 0 so the program stops after drawing 2/3rds even though I have an if statement which prevents drawing off screen.


Code:

ClrDraw
For I,-81,0,81
For J,-81,81,81
If I≠0 or J≠0:Then
For G,-27,27,27
For H,-27,27,27
If G≠0 or H≠0:Then
For E,-9,9,9
For F,-9,9,9
If E≠0 or F≠0:Then
For C,-3,3,3
For D,-3,3,3
If C≠0 or D≠0:Then
For A,-1,1,1
For B,-1,1,1
If A≠0 or B≠0:Then
A+C+E+G+I+121→Y
B+D+F+H+J+132→X
If Y≥0 and Y≤164:Then
Pxl-On(Y,X,RED)
End:End:End:End
End:End:End:End
End:End:End:End
End:End:End:End



ClrDraw
For I,-1,1,1
For J,-1,1,1
If I≠0 or J≠0:Then
For G,-3,3,3
For H,-3,3,3
If G≠0 or H≠0:Then
For E,-9,9,9
For F,-9,9,9
If E≠0 or F≠0:Then
For C,-27,27,27
For D,-27,27,27
If C≠0 or D≠0:Then
For A,-81,0,81
For B,-81,81,81
If A≠0 or B≠0:Then
A+C+E+G+I+121→Y
B+D+F+H+J+132→X
If Y≥0 and Y≤164:Then
Pxl-On(Y,X,RED)
End:End:End:End
End:End:End:End
End:End:End:End
End:End:End:End
Weregoose wrote:
Sierpinski Triangle
Inputs: None
Outputs: IFS-generated Sierpinski sieve fractal

Code:
:0
:Repeat 0
:.5(Ans+e^(.5iπint(3rand
:Pt-On(real(Ans),imag(Ans
:End

Evil or Very Mad
mr womp womp

Thanks for the response. Unfortunately, the code doesn’t work. At first I was getting an error, then I figured I should try setting the calc to radians. The code ran, but all it does is put a couple of dots in the center of the screen. I let it run for awhile, but nothing but a few dots. Anyways, your response comment says Sierpinski Triangle. I’m drawing a Sierpinski square. I would try for a Sierpinski cube, but I’m not sure how well it would show on the calculator. I think the TI84+CE can do 3D, haven’t look into it.
In my code, if I remove the If statement just before the Pxl-On statement and one of the End statements, it runs faster and takes 5min, 29seconds. Since I limit the last 1/3rd of the square in one of the FOR statements, I can eliminate that If statement since the program ends before it tries to plot off screen.
dave1707 wrote:
mr womp womp

Thanks for the response. Unfortunately, the code doesn’t work. At first I was getting an error, then I figured I should try setting the calc to radians. The code ran, but all it does is put a couple of dots in the center of the screen. I let it run for awhile, but nothing but a few dots. Anyways, your response comment says Sierpinski Triangle. I’m drawing a Sierpinski square. I would try for a Sierpinski cube, but I’m not sure how well it would show on the calculator. I think the TI84+CE can do 3D, haven’t look into it.

Yeah your window settings are probably wrong.
Make sure Xmin=-1, Xmax=1, Ymin=0, Ymax=1.

mr womp womp Thanks. I don’t know what the last thing I ran that changed the values, but they were like +/- in the thousands. I don’t play with the calculator that often, so I don’t think of looking at the graph values.
For posterity, my code that got posted above already had an update three years later.

Edited to add: Tweaking said code gives the Sierpinski carpet as:


Code:
:1
:Repeat 0
:Ans/3+iPart(2i^(.5int(8rand
:Pt-On(real(Ans),imag(Ans
:End
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