Guide to Cczcpaczcp Part 1

Saturn and Titan contain a fractal type I’ve chosen to call Cczcpaczcp, the name looks bizarre and frankly I think it needs a better name. There is a reason for the name and that is that it is constructed from the formula as follows constant, constant, z, complex power which takes care of the first five letters “Cczcp” then it’s add, constant, z, complex power giving “aczcp”, putting them together gives Cczcpaczcp and a rough indication of the formula not taking into account brackets.

This is the formula tab showing the fractal default parameters:

The initial value used can’t be zero as every iteration will evaluate to zero and no fractal will be produced. This leaves a choice of setting a non-zero initial value or using the location in the complex plane.

This is what you get using the location in the complex plane as the initial value and using 16 as the bailout limit.

There is a large spot at the centre of the fractal, increasing the bailout value by adding zeros to bailout limit will result in the following image with a bailout value of 1600000:

At the end of the limbs there are two black areas, zooming in on one gives:

The black area looks like a heavily mangled Mandelbrot, so can this fractal produce Mandelbrots? Yes it, can. To do so requires changes to the values of alpha and gamma, after experimentation it was found that setting both to 0.5 produces the following:

There is a similar picture in an earlier post, the difference is due to the bailout value being 16 instead of the 1600000 I set earlier. There is also an other difference and that is the use of a fixed initial value instead of the location in the complex plane.

The next part will deal with the use of fixed initial values and the “critical” value in particular.

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