I’m currently writing a Saturn User Guide to be included in the Saturn package when Saturn is released and along with the user manual is the only thing that is holding back the release of Saturn and Titan.
The Saturn User Guide aims to give user’s of Saturn a starting point for various fractal types, eventually the guide will feature all the fractal types implemented in Saturn, the initial version will point the way where guidance is needed as it can be very frustrating being presented with a fractal type and a very uninteresting initial image (in some cases it may be a single colour rectangle), it will also include a guide to some other fractals for which guidance isn’t so pressing.
As hints and tips for Saturn can also apply to other fractal programs, I will publish here portions of the Saturn User Guide starting with the Compasses fractal. The fractal type is implemented in Saturn as:
z <- transform(z)
z <- zalpha – alpha*c(alpha – 1)*z + beta
Of course the transform line only applies to Saturn, in this post there are no transforms applied to the Compasses formula.
It can be seen from the formula that the initial value of z (z0) can not be zero if beta is also zero. Using alpha = 2, beta = 0 and z0 = 1 we get the following image which isn’t that interesting.
I’m not going to explore the Compasses fractal with z0 = 0 and varying values of beta because changing the value of z0 to the location in the complex plane is much more interesting. With z0 = c we get this:
Changing beta leads to some interesting effects:
beta = 0.0875
beta = -1
beta = -1.665 (Rotated 90 degrees)
So, that’s it for part 1, in part 2 I’ll show examples of Inverse Compasses, i.e. apply the power transform to the complex plane using a power of -1. In part 3: Compasses with a negative value for alpha and finally in part 4: imaginary values for alpha.
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