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Description
The images are from the Symmetric Icons formula.
Traditionally, this formula is used for rendering the symmetric icons strange attractors in 2D, and in some cases, in 3d (in Chaoscope, for example).
Instead of doing that, I ported the formula to 3D using the spherical coordinates, in the same way that the mandelbulb works, since both are symmetric fractals.
For every symmetric strange attractor, there's a 3D version of it in this way, and the resulting shapes can be very interesting. The attractor itself resides on the centers of these shapes, I still didn't have visualized it, but that's a matter of time.
Some of the images are calculated using the old zbuffer method, the others are from a different method, more or less like the distance estimator, but that allow me to explore every escape time fractal formula without calculating the distance estimator itself.
If anyone is interested on the formula, please let me know, and I will post it.
Now it's time to go back to the land of the living..
Traditionally, this formula is used for rendering the symmetric icons strange attractors in 2D, and in some cases, in 3d (in Chaoscope, for example).
Instead of doing that, I ported the formula to 3D using the spherical coordinates, in the same way that the mandelbulb works, since both are symmetric fractals.
For every symmetric strange attractor, there's a 3D version of it in this way, and the resulting shapes can be very interesting. The attractor itself resides on the centers of these shapes, I still didn't have visualized it, but that's a matter of time.
Some of the images are calculated using the old zbuffer method, the others are from a different method, more or less like the distance estimator, but that allow me to explore every escape time fractal formula without calculating the distance estimator itself.
If anyone is interested on the formula, please let me know, and I will post it.
Now it's time to go back to the land of the living..
Image size
3072x1024px 3.95 MB
© 2015 - 2024 Aexion
Comments3
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Found a base formula
It is "easily extendable" to lots of new variants... there are many squarings available now - amazing idea
zbar=sqr(x)+sqr(y)
p=alpha*zzbar+lambda
zreal=x
zimag=y
for i=1 to degree-2 do
begin
za=zreal*x-zimag*y
zb=zimag*x+zreal*y
zreal=za
zimag=zb
end
zn=x*zreal-y*zimag
p= p+beta*zn
xnew= p*x+gamma*zreal-omega*y
ynew= p*y-gamma*zimag+omega*x
x=xnew
y=ynew
It is "easily extendable" to lots of new variants... there are many squarings available now - amazing idea
zbar=sqr(x)+sqr(y)
p=alpha*zzbar+lambda
zreal=x
zimag=y
for i=1 to degree-2 do
begin
za=zreal*x-zimag*y
zb=zimag*x+zreal*y
zreal=za
zimag=zb
end
zn=x*zreal-y*zimag
p= p+beta*zn
xnew= p*x+gamma*zreal-omega*y
ynew= p*y-gamma*zimag+omega*x
x=xnew
y=ynew