Working with complex numbers

Julia has first-class support for complex number arithmetic. Coupling this with powerful comprehension functionality allows you to easily perform complex computations. In this recipe, we will show how to plot a Julia set.

Getting ready

Make sure you have the PyPlot.jl package installed. If it is missing run the using Pkg; Pkg.add("PyPlot") commands in the Julia command line.

We would like to count how many iterations are required for repeated application of a mapping 

  to reach a value whose norm is greater than two. The number of iterations depends on the point from which we start the iterations. We will plot a heat map showing this relationship. You can find more details about the Julia set at http://mathworld.wolfram.com/JuliaSet.html or https://en.wikipedia.org/wiki/Julia_set.

Note

In the GitHub repository for this recipe, you will find the commands.txt file that contains the presented sequence of shell and Julia commands.

Now open your favorite terminal to execute...