For those of my dear watches who use Tierazon, Flarium24, Iteration, and probably also Sterlingware, all software written by Stephen Ferguson, I’ll tell you that it’s quite possible to use the compass formula for integer exponents. Just go to the “Draw-menu” and select “Unique Editor Dialogue”, and there paste one of the below formulas,

z*z-(2*c*z)
z*z*z-(3*c*c*z)
z*z*z*z-(4*c*c*c*z)
z*z*z*z*z-(5*c*c*c*c*z)

in the line there where by default stands z*z+c (the standard Mandelbrot formula). The parenthesis are for the sake of causing the software to perform the arithmetic in correct order If you wanna color 1-periodic components in the way I’ve done, be sure that “N-set Method” is selected (either in the dialogue box or under the drawing menu). In Flarium24 it’s called “F-set Method”.

All this works because these software by default use z = c as first input when drawing parameter spaces. Because in the Mandelbrot formula you obtain z = c as first output (0 -> c -> c^2 + c, etc) this will work as well in that type of formulas. However in the Compass formula z = 0 as first input will NOT work (would give the orbit 0 -> 0 -> 0 etc for every c), so beware that “Zero-Init” is not selected in the “Draw menu” of Flarium24 or “View menu” of Tierazon!

In fact it was using Flarium24, when I got my PC in the beginning of 1998, I for the very first time obtained and even saw the compass for d = 3 and then the compasses for the other integer exponents

You can type some constant values when you have the “Unique Editor Dialoge” box open. It was in that way I for the first time were able to draw (a_real, a_imag) - planes for fixed b-parameters in the normal cubic formula z -> z^3 - 3a^2 z + b. Before that I had studied the b-planes for fixed a-parameters using some Mac software. It was in that time, when I became able to draw both the a- and b – planes (which are doubble perpendicular to each other) I come to my personal discovery narrated in my journal “ How surfaces intersect in 4D-space” [link]

After some year I and my friend Greenseng [link] got Ultra Fractal Inspired be me he wrote his first Cubic Parameterspace formula making it possible for me and everyone to explore ALL the six perpendicular 2D-systems of slices of this four dimensional parameter space Many thanks to him