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Mandelbrot.jl

This is a library written in Julia to compute Mandelbrot fractals, using multi-threading and optionally GPU computing.

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You can find more 4k images in the images folder of this repository.

Installation

Before you install this package, please download and install ArrayFire. Once you have rebooted your system you can continue with the installation.

Please clone/download this repository and than start Julia in the package folder, then type in the REPL:

using Pkg
Pkg.activate("./")
Pkg.instantiate()
using Mandelbrot

Examples

Computing a fractal

To create a fractal is as easy as this:

using Mandelbrot

cmap1 = Mandelbrot.cycle_cmap(:inferno, 5)        
xmin1 = -1.744453831814658538530        
xmax1 = -1.744449945239591698236        
ymin1 = 0.022017835126305555133        
ymax1 = 0.022020017997233506531 

fractal1_data = FractalData(
    xmin1,
    xmax1,
    ymin1,
    ymax1,
    width = Mandelbrot.w_4k,
    height = Mandelbrot.h_4k,
    colormap = cmap1,
    maxIter = 1500,
    scale_function = x -> x,
)

computeMandelbrot!(fractal1_data) 

display_fractal(fractal1_data, filename = "mandelbrot1.png")

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Interactive navigation

To find interesting coordinates, you can use the "interactive" navigator. To move you can use the functions move_right, move_left, move_up, move_down and you can zoom in or out using zoom:

cmap = Mandelbrot.cycle_cmap(:inferno, 5)
xmin = -2.2
xmax = 0.8
ymin = -1.2
ymax = 1.2

fractal0_data = FractalData(
    xmin,
    xmax,
    ymin,
    ymax,
    width = Mandelbrot.w_4k,
    height = Mandelbrot.h_4k,
    colormap = cmap,
    maxIter = 1500,
    scale_function = x -> x,
)

fractal0_data.maxIter = 50
preview_fractal(fractal0_data, scale = :linear)
Mandelbrot.move_center!(fractal0_data, -41, 0)

fractal0_data.maxIter = 500 #increas maximum number of iterations
Mandelbrot.zoom!(fractal0_data, 100)
Mandelbrot.move_left!(fractal0_data, 35)
Mandelbrot.zoom!(fractal0_data, 10)
Mandelbrot.move_left!(fractal0_data, 30, 0)
fractal0_data.maxIter = 1000
preview_fractal(fractal0_data, scale = x->1/log10(x)) #nice fractal!

coords = Mandelbrot.get_coords(fractal0_data) #let's save the coordinates for future use

Mandelbrot.set_coords(fractal0_data, coords...) #use this function if you want to quickly load some coordinates 

computeMandelbrot!(fractal0_data) # compute 4k resolution image
display_fractal(fractal0_data, scale = x->1/log10(x),
    filename = "images/mandelbrot_movement.png"
) #plot and save the fractal

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Animations

It is also possible to create an animation from a starting point (by default a zoomed out fractal) to an ending point in the following way:

xmin = 0.307567454839614329536
xmax = 0.307567454903142214608
ymin = 0.023304267108419154581
ymax = 0.023304267156089095573

Mandelbrot.create_animation((xmin, xmax, ymin, ymax), n_frames = 500, scale = log10, colormap = Mandelbrot.fire_and_ice())

You can see the resulting gif here (33Mb).

Progress

This is the first release of this library, much more work has to be done, currently I need to find a way to make smoother colormaps for the animations and implement correctly the perturbative theory computation schemes described at Wikipedia and mathr.co.uk. Any help and contribution is appreciated!