Print Page - New spherefold type?

Title: New spherefold type?
Post by: Alef on July 21, 2012, 07:13:02 PM

I was thinking about, well Holly Grail is an item to seak for. Alsou there could be another item to seek for, the Arc of Covenant, a perfect patern formula producing at least barnsley fern.

At least Tglad's formula could be a bitt modified;)

So I remembered power 8 (super)modulus function in complex numbers squaring the unit circle.
http://www.fractalforums.com/new-theories-and-research/higer-dimension-modulus-or-something-odd/ (http://www.fractalforums.com/new-theories-and-research/higer-dimension-modulus-or-something-odd/)
Spherefold of amazingbox uses modulus function, which can be defined with power 8. Maybe a tesseractofold or cuted cubefold. ( Power 3 modulus will generate assymetric fold, and power 4 will generate something in between power 8 and 2, but power 100 would not much differ from 8.)

Code:

else if (spherefold == "Power 8 modulus")
{
radius =((zx)^8 + (zy)^8+ (zz)^8)^(0.125);
	if (radius < (Min_R) ) 
	{
	temp = 1/(Min_R);
	}
	else if (radius < 1 && radius !=0)
	{
	temp = 1/(radius);
	} 
	else
	{
	temp = 1;
	}
}

f=1.5 r=0.6 s=2 produced prison cell fractal.
(https://sites.google.com/site/3dfractals/mandelbox8th/TestsBox6.jpg)

The same spot, but r=0.5 and iteration numbers set to 15:
(https://sites.google.com/site/3dfractals/mandelbox8th/TestsBox5.jpg)

And something greener and more vibrant made by the same 8th power spherefold
(https://sites.google.com/site/3dfractals/mandelbox8th/TestsBox3.jpg)

https://sites.google.com/site/3dfractals/mandelbox8th (https://sites.google.com/site/3dfractals/mandelbox8th)

p.s.

I think, there could be lots more sphere and box fold substitutions.

Title: Re: New spherefold type?
Post by: DarkBeam on July 21, 2012, 07:52:45 PM

It's already implemented in MB3D, check out ABoxVaryScale2. You can vary exponents as liked. :cantor_dance:

Title: Re: New spherefold type?
Post by: fractower on July 21, 2012, 09:18:41 PM

Interesting result. Since you have given up on spherical symmetry there is no reason to stick to Cartesian axes. Cubic symmetry also has 8 corner axis or the 12 edge bisecting axis that might be interesting to try.

For exampe the corner axis:
Let axis[4] be the 4 unit vectors (+-sqrt(3),+-sqrt(3), sqrt(3). Inversion symmetry gives you (+-sqrt(3),+-sqrt(3),-sqrt(3) for free.

Code:

else if (spherefold == "Power 8 modulus")
{
              radius=0;
              for(i=0;i<4;i++){
              radius += (Dot(z, axis[i]))^8;
              }


              radius =radius^(0.125);
	if (radius < (Min_R) ) 
	{
	temp = 1/(Min_R);
	}
	else if (radius < 1 && radius !=0)
	{
	temp = 1/(radius);
	} 
	else
	{
	temp = 1;
	}
}

Title: Re: New spherefold type?
Post by: Alef on July 24, 2012, 12:15:51 PM

Quote from: DarkBeam on July 21, 2012, 07:52:45 PM

It's already implemented in MB3D, check out ABoxVaryScale2. You can vary exponents as liked. :cantor_dance:

Probably trying all the formulas ang going to next didn't noticed;)

Title: Re: New spherefold type?
Post by: Alef on July 25, 2012, 05:46:36 PM

He he, ABoxVaryScale2 is practicaly the same. Just no loss of symmetry with power 3.

All other symmetries are much harder to implement and would need addition variables. Hexagonal symmetry would be interesting, like bee hive.

(http://www.ljplus.ru/img4/a/s/asdam/Mbox_modulus_asd.jpg)

Code:

Mandelbulb3Dv17{
Y.....c....s/...w....22..............1.......s1E................................
........................................kz1........Y./..................y.2...uE
..........UDE.../s.0/.....E.....s/....E5.....AANe04JGhqD/.......BJJ/0dkpXm1.F..6
z.....kD12../..........wz................................I.u1....y1...sD...../..
.z1...sDYsAIxzzzjz1..........WAbUdisqcljRRxgCKosEwnYRydIKa5uzwPN9SaPRGyDFHQlSHA1
Iw1iNMIOip7tzqF/G0ZZtVyD......oNM.............kD.2....sD..kz....................
.............oAnAr1...sD....zU/SU6.is/W.MZ560UTSU6.au/W.sg560UxSU6......B....k1.
.....MEUZz1.......kz.chqO1.U..6.P....M/...kD....i/...kB....F....8/...I1...kQTF5Q
...U.O3XhiRfMFnqM..XPXo9..6.5c..rTzx............/.........E..0........U.8.kXWF1.
.sM93P58iz9.MmnWK2zwz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................UgWL.Ufiu8.F.W4CK9.Sudb.g0EXMdZ.wtb
T0kBUNgbL..ecW8.mt5mHS/.Sudb.QfTGvL1..Dwk1EzyJxY9..wk1D..xrppZ..k1Dw.QsTLfK0..Dw
k1UmzBRXA..wk1D....s....zz/..wD.yz1.s0..xzJrf0..................................
E....6....E.....I....M....EE0x4SK3aQtBpMVlKNm.........................k/........
...................0./........yD........kz1..........YqPkLMmIJyD........6.2.....
................................................................................
.....................2.....3....2....wJMnFKMhFZQVtqQ............................
4MU/..........................................................xj........U.2.....
...../........0E...................wz...........................................
................................}

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Fractal Math, Chaos Theory & Research => (new) Theories & Research => Topic started by: Alef on July 21, 2012, 07:13:02 PM