wada fractal

[taj]

Here are two fractals I created using POVRay. I dont think these should enter the mathcomp as POVray is able to construct these fractals *without* any equations. Nontheless they are cute.The fractal is the reflection between 4 spheres (three in a triangle and one behind them). I've done a wide angle picture to show the three spheres in a triangle. Then a close up of the so-called wada fractal.

I wonder if it can be done in real time. The image is produced using raytracing and the number of ray bounces allowed here is 256 so it seems very unliekly to me.

[Shockwave]

Simply beautiful!

[Ghost^BHT]

I have tried that using bryce as a renderer and come up with less than good results - looks good using POV - 

[taj]

I have tried that using bryce as a renderer and come up with less than good results - looks good using POV - 

POVs brilliant.

[taj]

It turns out this fractal is very sensitive to the position of light in the scene and surface materials of the spheres. Here is a variation where I move the lights a fraction and add in some ambient reflection in the material (0.1). Alieneye - maybe the materials etc was a reason Bryce didnt produce good pictures?
The thing is DAMN sensitive to them!

[rdc]

Wow, simply amazing.

[taj]

And here just the material is changed, no lights moved ...

[Jim]

Are all the reflections perfectly specular, or are there diffuse reflections too?  Where are the lights?  What kind?  In terms of real-time, I reckon it might be possible to do *something*, maybe 8 reflections at 1fps or thereabouts.  I would aim to use 32bit floats, set the visual studio code-gen to produce SSE, multi-thread for HT/dualies, and rely on sphere normals being really easy to calculate.  I'd also not draw anything but the active pixels.  It'd be a challenge though.

Jim

[taj]

Are all the reflections perfectly specular, or are there diffuse reflections too?  Where are the lights?  What kind?  In terms of real-time, I reckon it might be possible to do *something*, maybe 8 reflections at 1fps or thereabouts.  I would aim to use 32bit floats, set the visual studio code-gen to produce SSE, multi-thread for HT/dualies, and rely on sphere normals being really easy to calculate.  I'd also not draw anything but the active pixels.  It'd be a challenge though.

Jim

Here is a POVRay file and the image it produces Jim

Code Select Expand


#include "colors.inc"

global_settings {
max_trace_level 256
max_intersections 256
}

// Camera specification
camera {
   location <2,-2,2>
   up       y
   right    x
   angle    10
look_at   <0,0,0>
}

// Three lights, red, green, blue located opposite four of the three gaps
light_source {
   <-0.1,-0.1,-0.1>
   color <1.0,0.5,0.7>
}
light_source {
   <-0.1,0.1,0.1>
   color <0.7,1.0,0.5>
}
light_source {
   <0.1,0.1,-0.1>
   color <0.5,0.7,1.0>
}

// The three spheres follow, all highly reflective and grey
sphere {
   <-0.5,-0.5,0.5>, 0.70710678118654757
   texture {
pigment {
color <1,1,1>
}
      finish {
ambient 0
diffuse 0.1
brilliance 1
                        specular 1
reflection 0.8
phong 1
phong_size 200
metallic
      }
   }
}
sphere {
   <0.5,0.5,0.5>, 0.70710678118654757
   texture {
      pigment {
         color <1,1,1>
      }
      finish {
         ambient 0
         diffuse 0.1
         brilliance 1
         specular 1
         reflection 0.8
         phong 1
         phong_size 200
         metallic
      }
   }
}
sphere {
   <-0.5,0.5,-0.5>, 0.70710678118654757
   texture {
      pigment {
         color <1,1,1>
      }
      finish {
         ambient 0
         diffuse 0.1
         brilliance 1
         specular 1
         reflection 0.8
         phong 1
         phong_size 200
         metallic
      }
   }
}
sphere {
   <0.5,-0.5,-0.5>, 0.70710678118654757
   texture {
      pigment {
        color <1,1,1>
      }
      finish {
         ambient 0
         diffuse 0.1
         brilliance 1
         specular 1
         reflection 0.8
         phong 1
         phong_size 200
         metallic
      }
   }
}


In general lights were placed further out (eg -3,-3,-3)...materials had more diffuse colouring (eg 0.8 ) but everything else remained the same...So lighting includes diffuse and in some cases ambient but reflections are purely specular...

[taj]

OK very last one, one light at the centre...

[Ghost^BHT]

Here's my attempt using Bryce to render - added some atmosphere too - I'll have to play around with the lighting and camera angle some

[taj]

really nice, like candy, did you have some transparency too or just reflection?

[Ghost^BHT]

Really like the one light render - No transparency just using mirror shader with mid ambiance levels set  and a background image gives it the colors - Doesn't look too fractal like 'cause of the camera angle I think. I will have to tweak this - How long did this take to render in POV ?  I haven't used POV since my old Amiga 500 died. The renders on that machine were measured in light years

[taj]

It takes about 90 seconds at 800x600 with 0.3 anti aliasing, usually I preview in 320x200 with no AA in about ten seconds...and yes I think the camera is critical to gettig a fractal look. What about Bryce, how long does it take?

I think Ill try to crunch down the single light one to 255 bytes and enter iti into the POVray size coding competition...it seems the most pleasant of the images to me.

[taj]

OK wish me luck ... I managed this image in 255 bytes:

Code Select Expand


#macro S(a,b,c)sphere{<a,b,c>,7.0710678
texture{pigment{color<1,1,1>}finish{ambient.1 diffuse.4 reflection.8}}} #end
global_settings{max_trace_level 256}camera{location-5 look_at 0}light_source{0,color<.5,.7,1>}
S(-5,-5,5)S(5,5,5)S(-5,5,-5)S(5,-5,-5)


Couldn't quite squeeze in everything in the original.

[taj]

Oh I rejected these two ... well ok, maybe I made the wrong choice, dont know. Anyway...thats all with wada ... like rdc keeps saying :-)

[rdc]

I think they are all quite cool. Great job!

[taj]

Another...

[slinks]

I have witnessed heaven and it comes in fractal form

[Rbz]

Yep, I like last one, nice colors