Fractal Dimension Of Julia Sets

Contents

Results

Colour Key

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Julia Sets

Im \ Re -2.625 -2.375 -2.125 -1.875 -1.625 -1.375 -1.125 -0.875 -0.625 -0.375 -0.125 +0.125 +0.375 +0.625 +0.875 +1.125 Re / Im
+1.875 +1.875
+1.625 +1.625
+1.375 +1.375
+1.125 +1.125
+0.875 +0.875
+0.625 +0.625
+0.375 +0.375
+0.125 +0.125
-0.125 -0.125
-0.375 -0.375
-0.625 -0.625
-0.875 -0.875
-1.125 -1.125
-1.375 -1.375
-1.625 -1.625
-1.875 -1.875
Im / Re -2.625 -2.375 -2.125 -1.875 -1.625 -1.375 -1.125 -0.875 -0.625 -0.375 -0.125 +0.125 +0.375 +0.625 +0.875 +1.125 Re \ Im

Benchmarks

Timings are in seconds, wall-clock elapsed time.

Julia
40962 20482 10242 5122 2562 1282 642 322
Image 10242 19615 6188 2163 1147 1081 659 189 162
5122 4662 1316 476 267 239 152 44 38
2562 1153 318 115 64 57 24 11 10
1282 286 80 29 16 13 6 2 2
642 72 20 7 5 4 2 1 1
322 19 6 2 1 2 0 1 1

Source Code

j-dim-render.c
Renders Julia sets and performs box-counting on GPU (using OpenGL 4).
j-dim-colour.c
Colours the raw box-counting data into various images.
j-dim-colour-key.c
Generates the images for the colour key.
j-dim.sh
Driver script that renders everything and generates this web page.

Detailed Results

Contents

Julia
40962 20482 10242 5122 2562 1282 642 322
Image 10242

Image 10242 Julia 40962

l0 \ l1 12 11 10 9 8 7 6 5 4 3 2 1
11
10
9
8
7
6
5
4
3
2
1
0

Image 10242 Julia 20482

l0 \ l1 11 10 9 8 7 6 5 4 3 2 1
10
9
8
7
6
5
4
3
2
1
0

Image 10242 Julia 10242

l0 \ l1 10 9 8 7 6 5 4 3 2 1
9
8
7
6
5
4
3
2
1
0

Image 10242 Julia 5122

l0 \ l1 9 8 7 6 5 4 3 2 1
8
7
6
5
4
3
2
1
0

Image 10242 Julia 2562

l0 \ l1 8 7 6 5 4 3 2 1
7
6
5
4
3
2
1
0

Image 10242 Julia 1282

l0 \ l1 7 6 5 4 3 2 1
6
5
4
3
2
1
0

Image 10242 Julia 642

l0 \ l1 6 5 4 3 2 1
5
4
3
2
1
0

Image 10242 Julia 322

l0 \ l1 5 4 3 2 1
4
3
2
1
0