More new Mandelbulb Variations

Rule 181 – Power 8 Mandelbulb

Rule 388 – Power 4 Juliabulb

Rule 404 – Power 2 Juliabulb

Rule 1328 – Power 4 Juliabulb

Rule 2160 – Power 8 Juliabulb

Rule 2512 – Power 2.9 Juliabulb

After the last success with new Mandelbulb variations I extended the possible search space. These variations are also created from formulas from Tad Boniecki. Three of his variations followed these same basic forms.

See this blog post for all the details of the previous new variations. The only change here is adding a second trig call to the Y component. So now, the possible variants follow the pattern

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

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

Convert these 12 possible combos into a 12 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 –

This bumps the total possible variations up to 4096. After letting the PC churn away for a few hours I had all possible variations with thumbnails (I have avoided posting all 4096 images to flickr this time).

After deleting the spikey and lathed results this got the count of possibles down to 1288.

Deleting all the assymetrical results got the count down to 266 possibles.

Then comes the difficult part. You get down to a bunch of symmetric bulbs that fall into catagories of similar shapes and styles. Culling down the least interesting out of a bunch of 10 or so very similar images sent me cross eyed. In the end I narrowed 4096 down to 27.

Rule 181