Mandelbrot Set (Variable Power) JavaScript Simulation Applet HTML5

This is yet another variation of the Mandelbrot Set, the latest of the Mandelbrot series, you could say.

This time, what varies is the power to which the complex number z is raised to in each iteration.

The standard Mandelbrot Set is iterated as follows:



However, in this simulation (link here), we define the algorithm as follows:

z(n+1) = z(n)^k + c, where k is a real number.

The value of k can be adjusted with either the slider, which allows the values to be set between 1 and 10, or with the field provided, which allows for any real value of k to be entered. This set is also called the Multibrot Set, as a portmanteau of "Multiple" and "Mandelbrot".

Disclaimer: Due to the colouring algorithm used, selecting negative powers will end up merely returning a monotone page of colour. We are currently working on implementing a better colouring algorithm for all our Mandelbrot Set simulations so that they can be viewed in their infinite majesty.

The default value of k is set to k = 10, and the set is as follows:

Fractal for k = 10

Zooming in to one of the bulbs at the top, you can see that the fractal remains equally rough, as shown:

Zoomed-in fractal for k = 10, a fascinating structure emerges

The other values of k produce interesting shapes as well, for instance, let k = 6:

Fractal for k = 6

 Feel free to play around with the powers for the Multibrot, but do be patient as this simulation is extremely calculation-intensive, and thus lag is expected. You have been warned. Have fun!