My Math Forum Fractal Program

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 February 2nd, 2012, 08:32 PM #1 Newbie   Joined: Feb 2012 Posts: 3 Thanks: 0 Fractal Program Not sure if this belongs here or in the mathematics in art and fractals section, but I am trying to make a "fractal" program. Here is my code– I used a generic language so it is easy-ish to read. I'm getting incorrect results for many numbers. Code: set X to ORIGINALVALUE (for example, 1+i) set bounded to true set n to 1 repeat 6 times set X to (X2 + X) (This is just the mandlebrot equation) If (absolute value of x is greater than 4) then set bounded to false end repeat Anyone know why it might not be working? I figure putting the original value through the mandlebrot equation six times is enough, and the 4 is got is from Wikipedia, which (i think) says the Mandlebrot set declares anything which reaches a value greater than 4 is "unbounded". Thanks!
 February 2nd, 2012, 08:55 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Fractal Program Does your language handle complex numbers properly? Is six iterations enough? Are you actually squaring, or are you doing something else? (Languages differ on how to represent exponentiation, so if you were in C for example you might write x^2 thinking it would square x where in fact that would take the bitwise XOR of x and 2.) Is the display not working properly, rather than the calculation?
February 4th, 2012, 06:49 PM   #3
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Re: Fractal Program

I'll answer the easy questions first. I'm programming on a TI-83 plus calculator. I am certain I am actually squaring the equation. (I actually had a mistake with the mandlebrot equation, but I fixed it now) The TI language mostly handles complex numbers properly– I'm not too worried about it. The code is pretty complex for the displaying aspect, so I wasn't sure– until I ran the function in its entirety. The strange blob that appears is clearly nothing like the Mandlebrot set, so it isn't a rotation, slide, or stretch of anything. That leaves
Quote:
 Originally Posted by CRGreathouse Is six iterations enough?
I guess I'll try it with more iterations. With just six, it took an hour and a half or so. With like 10 iterations, it'll probably take about 3 hours. Yikes. I hope I have enough batteries in the calculator. Thanks for all the help, I'll let you know if it works. If it doesn't, I think either I misinterpreted the numbers I got from Wikipedia or the TI calculators really do not handle complex numbers well.

February 6th, 2012, 06:13 AM   #4
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Re: Fractal Program

Quote:
 Originally Posted by boy129349 I guess I'll try it with more iterations. With just six, it took an hour and a half or so. With like 10 iterations, it'll probably take about 3 hours. Yikes. I hope I have enough batteries in the calculator. Thanks for all the help, I'll let you know if it works. If it doesn't, I think either I misinterpreted the numbers I got from Wikipedia or the TI calculators really do not handle complex numbers well.
Try graphing only a small part of the set and see what you get. That's probably the best way to debug the program.

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