Here’s a natural follow-up to my last post on the Mandelbrot set – an interactive Julia set explorer!

The Julia set corresponding to a particular point c = x + iy in the complex plane is defined as the set of complex numbers z that stay finite upon arbitrary iterations of the following function: f_{c}(z) = z^{2} + c. The Mandelbrot set, by comparison, is defined as the set of complex numbers c such that the value obtained by starting with 0 and iterating the function f_{c} arbitrarily many times converges.

What’s remarkable is now beautiful and complex the patterns that arise from this simple equation are. Take a look for yourself: just hover over a point to see its corresponding Julia set!

Resolution is preset at a value good for seeing lots of details and loading at a reasonable speed, but should you want to change it, controls are ‘E’ to increase it and ‘Q’ to decrease it. To reset to default, press ‘SPACE’.