For the development of each release I add new fractal types, to do this I need a source of formulae. Once such source is FractInt, which happily exists in a Linux Mint software repository under the name xfractint. It has a number of formulae which are calculated using a single orbit, i.e. calculation starts at a fixed point and the location of each subsequent iteration is plotted, Saturn and Titan don’t do this (not yet anyway …). The nearest method is the orbit plotting all the orbit of fractals generated using the Julia algorithm with each orbit starting at different location, this approach works well with the Attractors fractal type which is based on a formula for strange attractors.
A fractal type chosen for addition to Saturn and Titan is called “threeply” in xfractint’s fractal type menu.
Unlike Attractors this fractal does not work well when plotting a large number of orbits using the Julia algorithm. As the formula has been added to Saturn and Titan, it has four modes of operation, orbit plotted Julia algorithm, Julia algorithm, orbit plotted Mandelbrot algorithm and Mandelbrot algorithm, just because the orbit plotted Julia algorithm was a failure doesn’t mean that the formula should be abandoned.
At the size produced by xfractint the Julia algorithm fractal isn’t that interesting and doesn’t appear to have much going for it, zooming in reveals an entirely different picture:
The pictures above aren’t for Threeply but for Threeply 2, this is due to mistake in the initial implementation of Threeply, there was an addition where there should have been a substraction. I had saved a fractal picture as a seed file before I found the error, I fixed the error and later when I tried using the seed file to produce a higher resolution picture I got an entirely different picture. as I liked the original picture I added Threeply 2 with the error restored.
This is the picture produced using Threeply instead of Threeply 2, all other settings are the same:
Finally high resolution pictures (12000×12000) produced by Titan and scaled to 1000×10000 using Gimp:
I’ve added two other fractals of the same type as Threeply, Hopalong and Quadrup 2, Quadrup 2 suffers the same problem as Threeply regarding the orbit plotted Julia algorithm but not quite as bad. Because those orbit fractals don’t produce good results “Single Orbit” fractals will be added to Saturn and Titan, implementation of these fractals requires considerably more work than just simply adding new formulae, hopefully the results will be worth the effort.