Even More New Mandelbulb Variations

Rule 5101 – Power 5 Juliabulb
Mandelbulb Fractal

Rule 20955 – Power 6 Mandelbulb
Mandelbulb Fractal

Hybrid Mandelbulb
Mandelbulb Fractal

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

Mandelbulb Fractal

Rule 1334

Mandelbulb Fractal

Rule 1444

Mandelbulb Fractal

Rule 2980

Mandelbulb Fractal

Rule 5101

Mandelbulb Fractal

Rule 5613

Mandelbulb Fractal

Rule 6326

Mandelbulb Fractal

Rule 8575

Mandelbulb Fractal

Rule 8703

Mandelbulb Fractal

Rule 11262

Mandelbulb Fractal

Rule 13246

Mandelbulb Fractal

Rule 16795

Mandelbulb Fractal

Rule 17290

Mandelbulb Fractal

Rule 17856

Mandelbulb Fractal

Rule 20937

Mandelbulb Fractal

Rule 20955

Mandelbulb Fractal

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

Jason.

2 responses to “Even More New Mandelbulb Variations

  1. i like how you’ve systematically enumerated them, this is real science 🙂

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

    • You can see the initial 512 variations here

      CustomTrig Rule 377 NEGATIVE SIN(PHI) NEGATIVE SIN(THETA) NEGATIVE COS(PHI)

      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.

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