Diverging Latticework
Produced December 2010.
From a strict mathematical point of view this isn’t a fractal, as I understand it, but, it seems to be acceptable to apply the term to anything produced by a fractal generating program. This pattern is typical of the “Gaussian Integer” colouring method, it has coloured an area well away from the chaos at the blunt end of a Mandelbrot with the centre line roughly corresponding with the real axis.
Why I didn’t release some formulae for Ultra Fractal
When writing fractal software it can be difficult to know whether a mistake in coding has been made especially with unfamiliar fractal types. For this reason I like to try things out on Gnofract4D as it is freely available for Linux, Gnofract4D is capable of using Ultra Fractal ufm and ucl files but they don’t always work. I also occasionally run a trial version of Ultra Fractal the make sure the ufm files are correct.
Sometime ago I was preparing to release some formulae for use with Ultra Fractal, this didn’t happen and I’m now going to show why. The fractal type I originally named “unnamed” (it’s still unnamed) has the following formula:
z <- (z^alpha + c)/(z*(z^beta – c)^gamma)
This is the result
using these parameters
This is what Gnofract4D produces using the same parameters.
And this is the mess that Ultra Fractal Produces also using the same parameters.
I have no idea why Ultra Fractal chokes on this formula, so I really couldn’t release the formulae for public use.
Gnofract4D Gaussian Integer is Peculiar
When I was implementing my version of the Gaussian Integer colouring method I came across something very puzzling about the Gaussian Integer colouring method as implemented in Gnofract4D. This is what I get using Gaussian Integer for outer colouring, the fractal type is of course the Mandelbrot set.
The colouring method settings are shown below:
And this is what Gnofract4D produces (I’ve included the outer colour setting).
I’m pretty sure that Gaussian Integer is correctly implemented in Saturn (and Mars before it) because I get the same patterns with Ultra Fractal. The really curious thing about this is that Gnofract4D is using standard.ucl from Ultra Fractal to produce this image.
The next post will be on the subject of colour maps also known as gradients.
Element90 Fractals 