August | 2011 | Softology's Blog

Rule 5101 – Power 5 Juliabulb

Rule 20955 – Power 6 Mandelbulb

Hybrid Mandelbulb

After the previous encouraging results here and here I had to try the fully extended 32,768 possible permutations of these trig variations.

Theta and Phi are initialised by using

theta:=arctan2(z.y,z.x);
phi:=arcsin(z.z/radius);

The Triplex Algebra power function uses

x=radius*cos(phi)
y=radius*cos(theta)*cos(theta)
z=radius*sin(phi)*cos(phi)

Each of the trig components can be +/- sin/cos phi/theta.

Convert these 15 possible combos into a 15 digit binary number using the following rules for each digit from left to right;
1. 0 for X COS, 1 for X SIN
2. 0 for X Phi, 1 for X Theta
3. 0 for +, 1 for –
4. 0 for Y COS, 1 for Y SIN
5. 0 for Y Phi, 1 for Y Theta
6. 0 for +, 1 for –
7. 0 for 2nd Y COS, 1 for 2nd Y SIN
8. 0 for 2nd Y Phi, 1 for 2nd Y Theta
9. 0 for +, 1 for –
10. 0 for Z COS, 1 for Z SIN
11. 0 for Z Phi, 1 for Z Theta
12. 0 for +, 1 for –
13. 0 for 2nd Z COS, 1 for 2nd Z SIN
14. 0 for 2nd Z Phi, 1 for 2nd Z Theta
15. 0 for +, 1 for –

After letting my PC churn away for a few days I had the results of the 32,768 variations. Here are the 16 I found most interesting and/or unique.

Rule 420