The only orbit plotted fractals (orbit fractals for short) I’ve dealt with so far are Pickover Popcorn fractals. For the next release of Saturn & Titan I decided to try plotting the orbits of a Mandelbrot instead of colouring it in the many ways that are available for escape time fractals. I modified the code that handled Pickover Popcorn to add the Orbit Mandelbrot fractal type.
This is what I got with accumulation colouring (i.e. colour based on the number of times a location is visited by an orbit):
As the fractal is essentially a Mandelbrot I considered how to add transforms to orbit fractal code, I realised that I’d modified the wrong code, the escape time fractal code already supports transforms so I added orbit plotting as an option to the escape fractals. The upshot of this is that all the escape fractals could be plotted as orbit fractals and the Pickover Popcorn fractal types are no longer required, this is because there are Pickover Popcorn escape time variants: PP Mandelbrot 4F, PP Mandelbrot 6F, PP Julia 4F & PP Julia 6F, the Pickover Popcorn 4F & Pickover Popcorn 6F fractals can be produced using PP Julia 4F & PP Julia 6F with the julia ‘seed’ value set to zero. I reduced the number of fractals types by adding function parameters and now the number is being further reduced by the introduction of the orbit plotting option.
Here are some examples of more orbit fractals: