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

Rule 1334

Rule 1444

Rule 2980

Rule 5101

Rule 5613

Rule 6326

Rule 8575

Rule 8703

Rule 11262

Rule 13246

Rule 16795

Rule 17290

Rule 17856

Rule 20937

Rule 20955

All of these new variations are now avilable in Visions Of Chaos.

Jason.

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i like how you’ve systematically enumerated them, this is real science đź™‚

it’d be good to see what some of the characteristic “duds” look like, too.

You can see the initial 512 variations here

The duds were the spikey ones, the lathed ones and any of them that had a non-symmetric look. I skipped uploading the 4096 and 32768 variaitons for these latest two posts, but they tended to follow the same sort of variaitons for the bad ones. Spikey/lathed/asymmetric.

I have some more ideas to try other variations the next time I can leave my PC on for a few days to run through them all.

Jason.