new holy grail candidate

[cKleinhuis]

hi there,

i was playing around yesterday with the triplex numbers, and i came up with an idea that leads to significant whipped cream reduction

idea for triplex numbers:
transform a 3d coordinate to spherical coordinate, made up of a distance and 2 angles, then add the 2 angles together and multiply the distance to obtain a square operation

new idea:
the idea is slightly different: instead of directly calculating the 2 angles for the spherical coordinate, perform a complex multiplication with the xy components as if it is a normal
complex number, then use the new position of the point to obtain a second angle, or easier spoken create a complex number out of the y'z components, where y' now refers
to the already transformed y position of the number, perform a complex multiplication and write back the new real number to the transformed position

algorithm:

z.xyz ; our 3 component coordinate
z'new = complexMul(z.xy,z.xy)  ; perform a complex multiplication with xy components
tempcomplex=(z'new.y , z.z)
templcomplex=complexmul(tempcomplex,tempcomplex)
z.xyz=(z'new.x,templcomplex.x,templcomplex.y)
z+=pixel

attached are 2 images from the same zslice, at position 0.25/2 and position 0.75/2
the one is rendered using the method described above, and the other one is the mandelbulb2 triplex slice

[Kali]

Tried your formula with my NODE-Raytracer

Nice try but...

 

[cKleinhuis]

lol, great view, much whipped cream, but at least an interesting structure
try out power8 version as well

[Kali]

Some Julias are not bad, nice mountains

A bit like the RotJulia (wich is z.xy complex multiplication + 3D rotation)

[cKleinhuis]

do you have the script at hand ? and u use a bruteforce approach?

[Kali]

Yes, it's a brute-force, progressive render with random start point & binary search approach... please wait a bit I'll be uploading it soon

[cKleinhuis]

the structure does not look like i expected, i expected somehow more streaks that get thinner,
i am going to play around with this simple aproach, there are many possibilities to play with it,
i made as well tests for:

- use simple complex multiplication in polar form, but use z coordinate solely for determining the length of the number, the multiplication is then applied only on the complex xy part of the number, but the length is determined by all three parts length=sqrt( x^2+y^2+z^2)
- original idea was to express the triplex mathematics solely with complex numbers, this might work when normalizing the numbers before
- i want to try out simple interpolation of the 2 numbers, weighting them 1/2 and create 2 complex numbers out of a 3 component number via
c1=(x,y) c2=(y,z)

[DarkBeam]

For Kali; please share the formula (not the entire script just the x,y,z calculation) as I can't get this result but an awful stuff

It's unclear how you can get a Mset when you square y two times? ohhhh well

z.xyz ; our 3 component coordinate
z'new = complexMul(z.xy,z.xy)  ; y is squared
tempcomplex=(z'new.y , z.z)
templcomplex=complexmul(tempcomplex,tempcomplex) ; y is squared twice
z.xyz=(z'new.x,templcomplex.x,templcomplex.y)
z+=pixel

[cKleinhuis]

@darkbeam, the original idea had exactly that drawback, yes, the way you performed it is basically what i suggested at the beginning. which is why there is so much whipped cream, and the images created by kali used the julia method on this formula

the images above with the mset if i remember correctly where created with a slight modification of the formula, i did not publish the formula, and since my computer broke down a few monthes ago i am unsure if i can resolve it when havng a new computer and reactivating those old harddisk

[DarkBeam]

Uh, do you mean; you adjust the magnitude to the square of the current? That is easy to write

[cKleinhuis]

Uh, do you mean; you adjust the magnitude to the square of the current? That is easy to write

i modified the approach in the following way ( but it did not lead to any surprises )

for the z.xyz^2 variant:
- take the magnitude from the 3 component vector
- use the variant above to get 2 new complex numbers
- normalize the 2
- and scale them to the magnitude^2 of the 3 component vector

[Alef]

Third 2d image looks like my unite vector addition mandelbrot.

formula:
z=z^2+c
z=z+0.1*(z/|z|) //  with z/|z| being unit vector when |z| is modulus of z (not as in fractint).



First 2D image looks like when unit vector is substracted from mandelbrot. Look in EM.upr Unit vector or in LKM. They generate same things in 2d.
This means that there is some mathematical reason behind it.