Some simple, fun Julia code for generating Mandelbrot set related imagery. This was basically a "weekend project" and is more of a nice demonstration of Julia than anything else.
Everything here works simply by mapping the values of individual pixels. As such, the images may look a little "grainy" depending on how many iterations are used. This can be remedied either by doing more iterations (or plotting more points) or with some sort of image post-processing.
One can check if a complex number z (specifically, any Julia Number) is in the mandelbrot
set by doing
using Mandelbrot
z ∈ mandelbrotBy default membership in the set is estimated from 10^3 iterations (without any tests for
convergence). One can change the number of iterations by doing ∈(z, mandelbrot, n_iter).
One can generate the so-called "buddhabrot" image by doing
h = buddha(10^7) # "buddhabrot" of 10^7 points drawn from the uniform distribution
h₁ = buddha(𝓅, 10^7) # "buddhabrot" of 10^7 points drawn from distribution 𝓅When generating the "buddhabrot" a histogram is made of mandelbrot trajectories from some
number z. By default these numbers are drawn from a uniform distribution, but they can
be drawn from any other 2-dimensional distribution using the
Distributions.jl package.
Note that the generation of trajectories will take place on parallel threads, but the histogram is generated sequentially.
The "buddhabrot" is a simple histogram, and for this I created a simple histogram
function using a simple binary search. Both of these functions can be found in
src/utils.jl. The binary search seems to have fairly good performance, but I did not go
crazy optimizing it.
