Software for visualizing Julia sets

Question

I would like a program where I can enter any complex function and see its Julia set. I have not been able to find a web program which does this. Most have functions which are of a fixed type, and you can only vary certain parameters.

What software/online programs will allow me to view Julia set of whatever function I enter?

Answer 1

Software which lets the user enter the formula:

• It
• XAOS

Answer 2

First off, Julia sets are not defined for all complex functions. Even within the set of all functions where some notion of Julia set has been defined, the techniques used for one class of functions is likely different from the techniques used for another. For example, we might study polynomials, rational functions, entire functions, meromorphic functions, or perhaps other types. Thus, it makes sense that most software might focus on one type or another.

I've written some Javascript explorations of complex dynamics that you can find on my webspace. In particular, there is are links for both polynomials and rational functions. The functions are defined by entering lists of coefficients, so it's at least more general than playing with a parameter.

Of course, even within context of just quadratics, there are functions whose Julia sets are not computable and other Julia sets where a simple escape time algorithm requires more iterations than is feasible in a reasonable amount of time.

Answer 3

I am not sure if this qualifies as an answer, but I'm going to give it a shot anyway. I developed a Python library using NumPy and SymPy sometime last year to plot Julia sets corresponding to almost any complex-valued self-map.

Here's the GitHub repository. More usefully, the documentation has plenty of examples showing how the library can be used to compute fixed-points, compute orbits, plot filled (and "un-filled") Julia sets, plot orbits of critical points, and plot parameter spaces.