Print Page - Furan's corner

Title: Furan's corner
Post by: Furan on October 20, 2012, 11:54:01 AM

My latest work. Unfortunately my coloring scheme was not very good and I had to decolor/recolor it, so it is monotone.
And I should have added a noise function.
(http://furan.sweb.cz/Wall2012/MandelbulbDmono400.jpg)
Available in 1920x1920 and HQ 3840x3840 (4x4AA), 11MB
http://furan.sweb.cz/

I will try to zoom in as much as double precision allows me.
The concept of visualization with a glowing aura seems legit.

Title: Re: Furan's corner
Post by: Furan on October 25, 2012, 06:55:06 AM

MandelDonut Fractal.
Or maybe not a fractal after all, I'm not sure if it has stable orbits of any kind.
10 iterations, 1920x1440 (5x5 AA)
http://furan.sweb.cz/Wall2012/MandelDonutHD.jpg (http://furan.sweb.cz/Wall2012/MandelDonutHD.jpg)

Code:

rho2  = sqrt(x**2+y**2)
rho8 = ((rho2-2)**2+z**2)**4
phi    = 8*ATAN2(y,x)
theta = 8*ATAN2(z,rho2-2.)
x = (rho8*COS(theta)+2) * COS(phi) + x_0
y = (rho8*COS(theta)+2) * SIN(phi) + y_0
z = rho8*SIN(theta)                 + z_0

(http://furan.sweb.cz/Wall2012/MandelDonut400.jpg)

Title: Re: Furan's corner
Post by: Furan on October 30, 2012, 12:53:28 PM

Same fractal in black smoke.
(http://furan.sweb.cz/Wall2012/MandelDonutB400.jpg)
http://furan.sweb.cz/Wall2012/MandelDonutBHD.jpg (http://furan.sweb.cz/Wall2012/MandelDonutBHD.jpg) 1920x1440
http://furan.sweb.cz/Wall2012/MandelDonutB3840.jpg (http://furan.sweb.cz/Wall2012/MandelDonutB3840.jpg) 3840x2880 (6x6AA), 5MB

Title: Re: Furan's corner
Post by: Furan on January 16, 2013, 10:56:01 PM

Ok, now the true MandelDonut:
(http://furan.sweb.cz/Wall2013/MandelDonutVegas400.jpg)
http://furan.sweb.cz/ (http://furan.sweb.cz/) (1920x1440)
HiDef 7680x5760 is in progress, I will also try some zoom in.
I had this idea about an external region of space that would save some escaping trajectories and immediately thought about the toroid, as the new iteration of rho would go across the center and land safely inside again. I will try some more elaborate structures, like knots etc.

Code:

R=2
ni=0
RHO = sqrt(x^2+y^2)
rho = sqrt((RHO-R)^2+z^2)
phi    = ATAN2(y,x)
theta = ATAN2(z,RHO-R)
Cx   = rho*COS(theta) * COS(phi)  //This Cx,Cy,Cz adjustment is new. Now the fractal set has a volume, a well defined orbit trap.
Cy   = rho*COS(theta) * SIN(phi)
Cz   = rho*SIN(theta)

Iterate, while rho<2R+2
------------------
RHO = sqrt(x^2+y^2)
rho = ((RHO-R)^2+z^2)^4
phi   = 8.*ATAN2(y,x)
theta = 8.*ATAN2(z,RHO-R)
x = (rho*COS(theta)+R) * COS(phi) + Cx
y = (rho*COS(theta)+R) * SIN(phi) + Cy
z =  rho*SIN(theta)               + Cz
ni++
------------------
I didn't manage to derivate this, so I used:
step=min(max(1E-8; 0.05/ni/ni*0.5**ni); 0.05)
There hasn't been done much tweaking of this formula, so it's probably pretty inefficient.

Title: Re: Furan's corner
Post by: cKleinhuis on January 17, 2013, 09:20:59 AM

nice, hello and welcome to the forums btw :D

what do you use for rendering ? fragmentarium ?!

Title: Re: Furan's corner
Post by: Furan on January 17, 2013, 11:47:44 AM

I'm rendering in my own Fortran 77 program (I'm working on implementation of material models to FE-systems. Now only in F77, so it's a sort of an excercise.)

Title: Re: Furan's corner
Post by: Furan on February 05, 2013, 04:04:42 PM

After about 10 days on 6 cores, this is the result: 7680x5760 (5x5 AA)
http://furan.sweb.cz/Wall2013/MandelDonutVegas7680.jpg (http://furan.sweb.cz/Wall2013/MandelDonutVegas7680.jpg) 35MB

Title: Re: Furan's corner
Post by: cKleinhuis on February 09, 2013, 05:42:26 PM

you have been featured on orbittrap.ca ;)
http://orbittrap.ca/?p=4480

Title: Re: Furan's corner
Post by: Furan on February 10, 2013, 10:23:01 AM

Beautifully written. :) Thank you for the memo. I will definitely continue my work on this piece.

Title: Re: Furan's corner
Post by: Furan on February 22, 2013, 01:30:27 AM

Math background in http://www.fractalforums.com/theory/a-generalization-of-triplex-zpplusc/ (http://www.fractalforums.com/theory/a-generalization-of-triplex-zpplusc/)
Behold the Trifold MandelKnot:
(http://furan.sweb.cz/Wall2013/TrifoldMandelKnot960.jpg)
http://furan.sweb.cz/Wall2013/TrifoldMandelKnot.jpg (http://furan.sweb.cz/Wall2013/TrifoldMandelKnot.jpg) 1920x1920 (5x5 AA)
It's still work in progress. It looks biological, so I was wondering about coloring it as nerve bundle or an artery ripped out from a beating heart :evil1:
My initial attempts were not successful.

Title: Re: Furan's corner
Post by: Pauldelbrot on February 22, 2013, 04:31:18 AM

:thumbsup1:

I just had a thought about 3d Mandelbrots myself.

The points on a non-singular elliptic curve in the plane form an additive group under the operation "draw a line through two points on the curve (the tangent there if they're not distinct) and find the third intersection (or if it's tangent at one of the two points, that's the third)".

I wonder if there's some higher-dimensional analogue with three degrees of freedom and a reasonable multiplication operation that can be defined as well?

Title: Re: Furan's corner
Post by: Furan on March 08, 2013, 11:54:06 AM

The coloring is a bit too much. Watch your eyes :)
Trifold Julia Knot
(http://furan.sweb.cz/Wall2013/TrifoldJuliaKnot1080.jpg)

Title: Re: Furan's corner
Post by: Dinkydau on March 08, 2013, 09:49:16 PM

Nice work

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Fractal Art => Images Showcase (Rate My Fractal) => Topic started by: Furan on October 20, 2012, 11:54:01 AM