Logo by Pauldelbrot - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Check out the originating "3d Mandelbulb" thread here
 
Home Help Search Gallery Downloads Login Register
*
Welcome, Guest. Please login or register. October 03, 2018, 07:45:08 PM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Welcome to Fractal Forums > Fractal Art > Images Showcase (Rate My Fractal) > Furan's corner
Pages: [1]   Go Down
« previous next »
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: Furan's corner  (Read 1599 times)
Description: Fractals and other works with meshless rendering in Fortran
0 Members and 1 Guest are viewing this topic.
Furan
Explorer
****
Posts: 44



WWW
« 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.

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.
Logged
Furan
Explorer
****
Posts: 44



WWW
« Reply #1 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
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
Logged
Furan
Explorer
****
Posts: 44



WWW
« Reply #2 on: October 30, 2012, 12:53:28 PM »
Same fractal in black smoke.

http://furan.sweb.cz/Wall2012/MandelDonutBHD.jpg 1920x1440
http://furan.sweb.cz/Wall2012/MandelDonutB3840.jpg 3840x2880 (6x6AA), 5MB
Logged
Furan
Explorer
****
Posts: 44



WWW
« Reply #3 on: January 16, 2013, 10:56:01 PM »
Ok, now the true MandelDonut:

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.
« Last Edit: January 16, 2013, 10:59:05 PM by Furan » Logged
cKleinhuis
Administrator
Fractal Senior
*******
Posts: 7044


formerly known as 'Trifox'


WWW
« Reply #4 on: January 17, 2013, 09:20:59 AM »
nice, hello and welcome to the forums btw cheesy

what do you use for rendering ? fragmentarium ?!
Logged
---

divide and conquer - iterate and rule - chaos is No random!
Furan
Explorer
****
Posts: 44



WWW
« Reply #5 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.)
Logged
Furan
Explorer
****
Posts: 44



WWW
« Reply #6 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 35MB
Logged
cKleinhuis
Administrator
Fractal Senior
*******
Posts: 7044


formerly known as 'Trifox'


WWW
« Reply #7 on: February 09, 2013, 05:42:26 PM »
you have been featured on orbittrap.ca wink
http://orbittrap.ca/?p=4480
Logged
---

divide and conquer - iterate and rule - chaos is No random!
Furan
Explorer
****
Posts: 44



WWW
« Reply #8 on: February 10, 2013, 10:23:01 AM »
Beautifully written. smiley Thank you for the memo. I will definitely continue my work on this piece.
Logged
Furan
Explorer
****
Posts: 44



WWW
« Reply #9 on: February 22, 2013, 01:30:27 AM »
Math background in http://www.fractalforums.com/theory/a-generalization-of-triplex-zpplusc/
Behold the Trifold MandelKnot:

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  evil
My initial attempts were not successful.
Logged
Pauldelbrot
Fractal Senior
******
Posts: 2592



pderbyshire2
« Reply #10 on: February 22, 2013, 04:31:18 AM »
Repeating Zooming Self-Silimilar Thumb Up, by Craig

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?
Logged
My fractal videos.
Furan
Explorer
****
Posts: 44



WWW
« Reply #11 on: March 08, 2013, 11:54:06 AM »
The coloring is a bit too much. Watch your eyes smiley
Trifold Julia Knot
Logged
Dinkydau
Fractal Senior
******
Posts: 1616



WWW
« Reply #12 on: March 08, 2013, 09:49:16 PM »
Nice work
Logged

My gallery: http://dinkydauset.deviantart.com/gallery/
Pages: [1]   Go Down
« previous next »
  Print  
« previous next »
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
On the Corner Mandelbulb3D Gallery lenord 0 260 Last post August 06, 2010, 05:43:03 PM
by lenord
around the corner of the -1.5 2D box Mandelbulb3D Gallery bib 0 275 Last post November 23, 2010, 11:49:16 PM
by bib
The Corner Images Showcase (Rate My Fractal) Kali 2 744 Last post March 15, 2011, 06:06:08 PM
by Kali
Stuck In A Corner Mandelbulb3D Gallery haltenny 0 311 Last post March 25, 2011, 02:26:56 PM
by haltenny
Missing Corner Mandelbulb3D Gallery Kali 0 362 Last post March 30, 2011, 05:49:39 AM
by Kali

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.17 seconds with 24 queries. (Pretty URLs adds 0.013s, 2q)