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comment How to compute a negative "Multibrot" set?
However, if I apply your formula to the "original" Mandelbrot set z^2 + c, the result looks similar to the Mandelbrot set, but is disconnected for some reason.
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comment How to compute a negative "Multibrot" set?
I did use your ideas to improve my program. I would like if educators and others potentially interested in fractals knew about it...
May
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comment Checking for NaNs in asm.js code
When you wrote x = x, did you mean x == x?
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comment How to compute a negative "Multibrot" set?
I'm not surprised that division by 0 is not a problem :-) I studied a lot of math in college, but have been developing business software for the past six years. I got carried away with an example program that shows how to plot the Mandelbrot set, which is how I encountered this problem in the first place. Javascript uses 64-bit floating-point arithmetic and according to MDN, the smallest positive number it represents is about 5e-324, a very small quantity, indeed!
May
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comment How to compute a negative "Multibrot" set?
Thanks. Can you explain to me how you compoute Lyapunov exponents?
May
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comment How to compute a negative "Multibrot" set?
@Mark, I've taken some time to review your answer in its entirety. You use a lot of terminology from complex dynamics that is not familiar to me. However, from a programming point of view, you mention something problematic: the possibility of "landing on zero". In floating-point arithmetic, we really can't speak of landing on an exact number because of the inherent approximate nature of floating-point arithmetic. All the above being said, I was able to modify my program to produce a graph similar to yours by checking for periodicity. (using approximate equality)
May
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comment How to compute a negative "Multibrot" set?
I just fixed an error in the Mandelbrot definition above: a point is in the set if and only if the sequence generated by that point is bounded. The question previously said "convergent", and that definition does not allow for generalization to negative multibrot sets. I can't recall if I made this mistake or if it was introduced by one of the editors, but this is an important distinction!
May
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revised How to compute a negative "Multibrot" set?
correct Mandelbrot definition to say sequence must be bounded, not convergent
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comment How to compute a negative "Multibrot" set?
This is going to take a while for me to digest, but I would like to point out that we were in agreement from the beginning that no "escape radius" exists in the sense that it does with positive multibrot sets.
Apr
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asked How to compute a negative "Multibrot" set?
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