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May
6
comment What does a 3D periodic solution of a differential equation look like?
@2mkgz An amazingly incomplete response. I'd actually downvote, if you'd posted an actual answer. :)
May
6
answered What does a 3D periodic solution of a differential equation look like?
May
3
answered What Method is used for Projecting the Rauzy Fractal?
May
2
comment How to compute a negative “Multibrot” set?
@DanielAllenLangdon There is a floating point zero that can be produced by simple arithmetic, though, and division by that zero produces a problem. Nonetheless, I was surprised to find it to be a non issue when I coded it in JavaScript. I'm sure the code just misses that scenario due to the improbability of hitting it exactly.
May
1
comment How to compute a negative “Multibrot” set?
Very nice again - thanks!
May
1
comment How to compute a negative “Multibrot” set?
@DanielAllenLangdon Yes, you made it quite clear in your question that you had come to that conclusion after your implementation involving the erroneous bailout. I do hope that you find the mathematical discussion, outline of the algorithm, and Javascript implementation all described in the answer to be of use to you. It's an interesting family and I've certainly enjoyed thinking about it.
May
1
revised How to compute a negative “Multibrot” set?
added 955 characters in body
May
1
comment How to compute a negative “Multibrot” set?
If you don't mind me asking, how well does your Julia set algorithm work for $p=-2$ and $c=-1/2^{2/3}$?
Apr
30
comment How to compute a negative “Multibrot” set?
Very nice - makes good sense, too. Another approach to generating the Julia set is to simply iterate until you reach the attractive orbit. Since there's just one attractive orbit, you can find it at the outset by iterating from the critical point.
Apr
30
revised How to compute a negative “Multibrot” set?
added 104 characters in body
Apr
29
comment How to compute a negative “Multibrot” set?
@Zach466920 Thank you! If $p$ is not an integer, then the function is no longer rational and the analysis becomes much more complicated. If $p$ is not rational, then you'd need to move to the iteration of transcendental functions. There are results along these lines but the situation is really totally different. I would not expect to discover any nice behavior by treating $p$ as a parameter. I've been wrong before, though. :)
Apr
29
revised How to compute a negative “Multibrot” set?
added 229 characters in body
Apr
29
revised How to compute a negative “Multibrot” set?
edited tags
Apr
29
answered How to compute a negative “Multibrot” set?
Apr
29
comment Is the adjacency matrix of a given graph (OR any graphs isomorphic to a given graph) a Kronecker product, and if so what are the factors?
Welcome to the community. You might also be interested in mathematica.se. In either case, there are useful formatting tools for typeset mathematics and code. I edited your question to make the code more accessible. Have fun!
Apr
29
revised Is the adjacency matrix of a given graph (OR any graphs isomorphic to a given graph) a Kronecker product, and if so what are the factors?
added 616 characters in body
Apr
25
revised How can the Hausdorff measure be nonzero?
edited tags
Apr
23
comment how do i prove that a collection of contractions does not satisfy the open set condition?
To be more blunt, could you please present the IFS that you are working with? The question is interesting and potentially challenging. Given the IFS, someone might very well be interested in the challenge. Without it, certainly no one can answer your question.
Apr
22
comment how do i prove that a collection of contractions does not satisfy the open set condition?
I believe this is a very difficult problem from a purely algorithmic perspective and that there is no known, general algorithm. It might be possible to address your question specifically, if you could present the four functions that comprise the IFS.
Apr
22
comment This one wierd trick integrates fractals. But does it deliver the correct results?
@Zach466920 Cool! I agree with your $2/3$ computation. I guess I'm assuming that your set looks something like this. If you're a Mathematica user, I have Mathematica code that automates self-similar integration procedure.