Alexander's Horned Sphere

[DarkBeam]

Anyone has an idea on how to implement it as a formula (obviously not all the passages, just the final shape)? Even a DIFS one?

<a href="http://www.youtube.com/v/Pe2mnrLUYFU&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Pe2mnrLUYFU&rel=1&fs=1&hd=1</a>

[Mrz00m]

it looks like a tree fractal... with specific angles, i cant remember the name of that tree formula! why isnt there a tree plant IFS in the 3d programs?

[DarkBeam]

Yes; the problem is only that the branches are curved, they have an odd spin and they partially overlap. It's a bit more complicated than a normal tree ...

[Mrz00m]

hey i found something fairly similar, don't know if it is a fractal but it's pretty amazing:
http://k3dsurf.s4.bizhat.com/k3dsurf-ftopic119-15.html

includes code.

[Mrz00m]

and this one:
http://schmiegel.deviantart.com/art/dunno-256071127

and:
http://www.google.co.uk/search?q=shmiegel&um=1&ie=UTF-8&hl=en&tbm=isch&source=og&sa=N&tab=wi&ei=A3B8T87DH5GEhQf1-qWrDA&biw=1222&bih=704&sei=BXB8T6_CJsmHhQfw6JGtDA#um=1&hl=en&safe=off&tbm=isch&sa=1&q=schmiegel&oq=schmiegel&aq=f&aqi=g4g-m1g-S1g-sS3g-S1&aql=&gs_l=img.3..0l4j0i5j0i24j0i10i24l3j0i24.4274l4274l0l4552l1l1l0l0l0l0l137l137l0j1l1l0.frgbld.&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.,cf.osb&fp=25d2af04422dfdb2&biw=1222&bih=728

and:
http://www.google.co.uk/search?q=shmiegel&um=1&ie=UTF-8&hl=en&tbm=isch&source=og&sa=N&tab=wi&ei=A3B8T87DH5GEhQf1-qWrDA&biw=1222&bih=704&sei=BXB8T6_CJsmHhQfw6JGtDA#um=1&hl=en&safe=off&tbm=isch&sa=1&q=schmiegel+3d&oq=schmiegel+3d&aq=f&aqi=&aql=&gs_l=img.3...46144l47361l2l48038l3l3l0l1l0l0l90l176l2l2l0.frgbld.&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.,cf.osb&fp=25d2af04422dfdb2&biw=1222&bih=728

[Mrz00m]

hey one way they could have rendered that horned sphere totally smooth was with thousands of iterations of spheres so close together that it looks smooth, same as here:
http://www.math.kit.edu/iag5/lehre/s_diffgeo_2012s/de

[DarkBeam]

hey one way they could have rendered that horned sphere totally smooth was with thousands of iterations of spheres so close together that it looks smooth, same as here:
http://www.math.kit.edu/iag5/lehre/s_diffgeo_2012s/de

Nice attempts, but no formulas at all

[cKleinhuis]

is it just me but i always read "alexander's horny sphere" ....

[DarkBeam]

I bet you are a big fun of my forbidden fractal MandelBoobs ... It was just a joke

[cKleinhuis]

 

[Mrz00m]

MandelBoobs? where!

sorry, actually the code on the kdsurf forum are is extensions to a k3dsurf sample file called gyroid. http://k3dsurf.sourceforge.net/ perhaps also you could mail schmiegel on deviant art to ask him if he has some code for blender etc in C++   

[Mrz00m]

this page has a fractal style thing at the end, http://forums.cgarchitect.com/15503-new-moebius-ring-torolf-31.html

and this:

http://www.google.co.uk/search?q=k3dsurf+fractal&um=1&ie=UTF-8&hl=en&tbm=isch&source=og&sa=N&tab=wi&ei=O_F9T7WyINKWhQftlvnkDQ&biw=1226&bih=704&sei=PfF9T7u2E5GXhQe6yLGTDg#um=1&hl=en&safe=off&tbm=isch&sa=1&q=k3dsurf+moebius&oq=k3dsurf+moebius&aq=f&aqi=&aql=&gs_l=img.3...12753l14441l4l14593l7l7l0l7l7l0l0l0ll0l0.frgbld.&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.,cf.osb&fp=f1b516e7922117d&biw=1226&bih=728

THis guy's gallery:     
http://www.evolution-of-genius.de/gallery/default2.htm

[Syntopia]

I imagine you could do it in Structure Synth. I tried, but I'm too tired to find the right parameters.

Code:

set background #fff
set maxdepth 800

 r0
{ rz -180 } r0

rule r0  md 140 > r1 {
  { x 0.09 ry 1 s 0.9970}  r0 
   sphere
}

rule r1 {
{ rx 90  ry -90 s 0.7 }  r0
{ rx -90 ry -90 s 0.7   }  r0
}

set raytracer::samples 8

// dof is depth-of-field.
// Use 'Edit | Show 3D Object Information' to find the correct plane 
// comment the line below to disable this.
set raytracer::dof [0.024,0.02]

// Set materials either globally,
// or for a selected tag (e.g. 'shiny')
set raytracer::shiny::reflection 0.3
set raytracer::phong [0.5,0.6,0.2]