Tag Archives: Julia set

How to draw fractals in LaTeX

Mandelbrot set

Fractals are mathematical sets showing a repeating pattern at every scale. Fractal patterns are fascinating and are commonly found in nature, for example in cauliflowers, broccoli, lungs, or trees.

LaTeX can generate complex fractals with few lines of code but needs some packages to do that. So let’s prepare the LaTeX environment from scratch by installing all the necessary packages (and prepare a cup of coffee in the meantime):

The standalone package needs to be installed manually as it is not currently present in the Ubuntu repositories:

I noticed that PDF readers like evince and okular do not always show the generated fractals in high definition whereas Adobe Reader always does. If you experience the same issue install Adobe Reader:

The first fractal I am going to draw is the Mandelbrot set. Here is the LaTeX code using the tikz package:

To compile the tex file from the command line you can use the latexmk utility  previously installed.  I noticed that evince and okular don’t show this fractal in high definition so it’s better to open it with Adobe Reader.

The fractal looks like this (and like this in PDF):

Mandelbrot set
Mandelbrot set

Another approach is to use the pst-fractal package based on  the PSTricks package which is more powerful (but slower to compile) than the tikz package. Here is the code using pst-fractal:

You should compile it with xelatex and wait a bit more until you get the message Output written on filename.pdf (1 page) . This time you can open it in high definition also with evince or okular:

And this is the result in full colour (here is the PDF):

Mandelbrot set
Mandelbrot set in colour

I am now going to draw the Julia set. Again, I use the pst-fractal package. Here is the LaTeX code:

Compile it with xelatex as usual (and go for a cup of tea):

Here is the result (and here is the PDF):

Julia set
Julia set

Sources:

Mihalis Tsoukalos, LaTeX: Make text beautiful, Linux Format 201, Summer 2015

http://tex.stackexchange.com/questions/39474/generate-mandelbrot-images-using-tikz