Fractal Dimension Of Julia Sets

Contents

• Results
• Colour Key
• Julia Sets
• Benchmarks
• Source Code
• Detailed Results

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.

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