SDL Fractals
Fractal Image Generators in SDL
GitHub Repository
https://github.com/daelsepara/sdl-fractals
Building (Unix/Linux)
cd repository/src
make
Dependencies: sdl2, sdl2-image
Usage
./Fractals.exe /PARAMS={parameters.json} /IMAGE={image.png} /PALETTE={palette.json} /BENCHMARK {other parameters}
Required parameters
/PARAMS={parameters.json} or /PARAMETERS={parameters.json}
Read parameters from {parameters.json} file.
See parameters/ for sample parameter files.
Optional parameters
/IMAGE={image.png}
Save fractal to {image.png}
/PALETTE={palette.json}
Use {palette.json} colormap. See palettes/ for some colormaps that can be used.
/BENCHMARK
Generate fractal in memory without rendering on the screen or saving image to {image.png}
Without /BENCHMARK and /IMAGE, the fractal is rendered on the screen.
Other parameters
/INVERTX
Inverts x-axis. Left to right goes from + to - values.
/INVERTY
Inverts y-axis. Top to bottom goes from - to + values.
/INVERT
Inverts color values.
/LOG
Use log-scale color mapping. Overrides color mapping in parameter file.
/NORMALIZED
Use normalized color mapping. Overrides color mapping in parameter file.
/MOD
Use moduluo-255 color mapping. Overrides color mapping in parameter file.
/HISTOGRAM
Use histogram color mapping. Overrides color mapping in parameter file.
/DEFAULT
Use default color mapping. Overrides color mapping in parameter file.
Examples
Mandelbrot Set
Parameters
| Generator | z^exp + C |
| exponent | 2 |
| max iterations | 255 |
| escape value | 4.0 |
| parameter files | mandelbrot, mandelbrot2, mandelbrot3 |
| palette | default |
| source(s) | Mandelbrot.hpp, Mandelbrot2.hpp, Mandelbrot3.hpp |
Benchmarks
mandelbrot
Time (mean ± σ): 474.8 ms ± 7.7 ms [User: 450.3 ms, System: 17.9 ms]
Range (min … max): 460.1 ms … 484.7 ms 10 runs
mandelbrot2
Time (mean ± σ): 382.1 ms ± 7.6 ms [User: 359.3 ms, System: 17.4 ms]
Range (min … max): 375.8 ms … 401.5 ms 10 runs
mandelbrot3
Time (mean ± σ): 390.9 ms ± 11.6 ms [User: 365.0 ms, System: 18.2 ms]
Range (min … max): 376.6 ms … 411.8 ms 10 runs
Newton
Parameters
| Generator | z - (z^3 - 1)/(3z^2) |
| tolerance | 1e-6 |
| max iterations | 255 |
| parameter file | newton1 |
| palette | default |
| source | Newton1.hpp |
Time (mean ± σ): 868.1 ms ± 8.0 ms [User: 822.9 ms, System: 35.2 ms]
Range (min … max): 855.1 ms … 882.9 ms 10 runs
Julia Sets
Common Parameters
| Generator | z^exp + C |
| max iterations | 255 |
| escape value | 4.0 |
| source | Julia.hpp |
Specific Parameters and Benchmarks
| C | -0.4 + 0.6i |
| parameter file | julia1 |
| palette | magma |
Time (mean ± σ): 821.6 ms ± 8.3 ms [User: 770.7 ms, System: 38.7 ms]
Range (min … max): 812.3 ms … 836.7 ms 10 runs
| C | -0.8 + 0.156i |
| parameter file | julia2 |
| palette | inferno |
Time (mean ± σ): 936.7 ms ± 10.5 ms [User: 881.0 ms, System: 39.5 ms]
Range (min … max): 925.1 ms … 959.9 ms 10 runs
| C | 0.285 + 0.01i |
| parameter file | julia3 |
| palette | moreland |
Time (mean ± σ): 732.1 ms ± 12.2 ms [User: 678.0 ms, System: 38.8 ms]
Range (min … max): 718.5 ms … 755.8 ms 10 run
| C | -0.7269 + 0.1889i |
| parameter file | julia4 |
| palette | magma |
Time (mean ± σ): 1.224 s ± 0.019 s [User: 1.166 s, System: 0.041 s]
Range (min … max): 1.201 s … 1.263 s 10 runs
| C | 0.26294324588 - 0.0024215732998i |
| max iterations | 320 |
| normalized colormap | true |
| parameter file | julia5 |
| palette | inverted jet |
Time (mean ± σ): 3.495 s ± 0.027 s [User: 3.428 s, System: 0.039 s]
Range (min … max): 3.454 s … 3.544 s 10 runs
Mandelbrot4
Parameters
| Generator | z^exp + C |
| exponent | 4 |
| max iterations | 255 |
| escape value | 4.0 |
| parameter file | mandelbrot4 |
| palette | default |
| source | Mandelbrot.hpp |
Time (mean ± σ): 3.937 s ± 0.055 s [User: 3.831 s, System: 0.056 s]
Range (min … max): 3.898 s … 4.063 s 10 runs
Burning Ship
Parameters
| Generator | (Re(Zn) + iIm(Zn))^2 + C |
| inverted x | true |
| inverted y | true |
| normalized colormap | true |
| inside color | 0 |
| max iterations | 100 |
| escape value | 4.0 |
| parameter file | burningship |
| palette | hot |
| source | Mandelbrot.hpp |
Time (mean ± σ): 559.9 ms ± 4.1 ms [User: 518.1 ms, System: 33.7 ms]
Range (min … max): 552.8 ms … 567.2 ms 10 runs
Burning Ship (2)
Parameters
| Generator | (Re(Zn) + iIm(Zn))^2 + C |
| inverted x | true |
| inverted y | true |
| log colormap | true |
| inside color | 0 |
| max iterations | 100 |
| escape value | 4.0 |
| parameter file | burningship2 |
| palette | plasma |
| source | Mandelbrot.hpp |
Time (mean ± σ): 1.469 s ± 0.289 s [User: 0.840 s, System: 0.054 s]
Range (min … max): 1.248 s … 2.128 s 10 runs
Burning Ship (3)
Parameters
| Generator | (Re(Zn) + iIm(Zn))^2 + C |
| inverted x | true |
| inverted y | true |
| log colormap | true |
| inside color | 0 |
| max iterations | 100 |
| escape value | 4.0 |
| parameter file | burningship3 |
| palette | bluered |
| source | Mandelbrot.hpp |
Time (mean ± σ): 1.469 s ± 0.289 s [User: 0.840 s, System: 0.054 s]
Range (min … max): 1.248 s … 2.128 s 10 runs
Tricorn
Parameters
| Generator | (z_x^2 + z_y^2) - i(2 * z_x * z_y) + C |
| inside color | 0 |
| max iterations | 255 |
| escape value | 4.0 |
| parameter file | tricorn |
| palette | parula |
| source | Tricorn.hpp |
Time (mean ± σ): 575.8 ms ± 21.6 ms [User: 528.1 ms, System: 36.5 ms]
Range (min … max): 536.0 ms … 602.0 ms 10 runs
Multicorn
Parameters
| Generator | Z_bar^exp + C |
| exponent | 4 |
| inside color | 0 |
| max iterations | 255 |
| escape value | 4.0 |
| parameter file | multicorn |
| palette | viridis |
| source | Mandelbrot.hpp |
Time (mean ± σ): 1.316 s ± 0.016 s [User: 1.261 s, System: 0.040 s]
Range (min … max): 1.293 s … 1.346 s 10 runs
Barnsley Fern
Parameters
| Generator (xn) | xn = xx * x + xy * y + xc (see below) |
| Generator (yn) | yn = yx * x + yy * y + yc (see below) |
| inside color | 128 |
| max iterations | 10000000 |
| parameter file | barnsleyfern |
| palette | green |
| source | IteratedFunctionSystem.hpp |
Generator
| Probability | Transformation [ xx xy yx yy xc yc ] |
|---|---|
| p < 0.01 | [ 0.000 0.000 0.000 0.160 0.000 0.000 ] |
| p < 0.86 | [ 0.850 0.040 -0.040 0.850 0.000 1.600 ] |
| p < 0.93 | [ 0.200 -0.260 0.230 0.220 0.000 1.600 ] |
| p < 1.00 | [ -0.150 0.280 0.260 0.240 0.000 0.440 ] |
Time (mean ± σ): 664.8 ms ± 9.4 ms [User: 621.5 ms, System: 33.5 ms]
Range (min … max): 648.1 ms … 676.3 ms 10 runs
Barnsley Fern (Culcita)
Parameters
| Generator (xn) | xn = xx * x + xy * y + xc (see below) |
| Generator (yn) | yn = yx * x + yy * y + yc (see below) |
| inside color | 128 |
| max iterations | 10000000 |
| parameter file | culcita |
| palette | green |
| source | IteratedFunctionSystem.hpp |
Generator
| Probability | Transformation [ xx xy yx yy xc yc ] |
|---|---|
| p < 0.02 | [ 0.000 0.000 0.000 0.250 0.000 -0.140 ] |
| p < 0.86 | [ 0.850 0.020 -0.020 0.830 0.000 1.000 ] |
| p < 0.93 | [ 0.090 -0.280 0.300 0.110 0.000 0.600 ] |
| p < 1.00 | [ -0.090 0.280 0.300 0.090 0.000 0.700 ] |
Time (mean ± σ): 637.9 ms ± 32.5 ms [User: 583.6 ms, System: 33.9 ms]
Range (min … max): 589.1 ms … 683.9 ms 10 runs
Barnsley Fern (Thelypteridaceae)
Parameters
| Generator (xn) | xn = xx * x + xy * y + xc (see below) |
| Generator (yn) | yn = yx * x + yy * y + yc (see below) |
| inside color | 128 |
| max iterations | 10000000 |
| parameter file | thelypteridaceae |
| palette | green |
| source | IteratedFunctionSystem.hpp |
Generator
| Probability | Transformation [ xx xy yx yy xc yc ] |
|---|---|
| p < 0.02 | [ 0.000 0.000 0.000 0.250 0.000 -0.400 ] |
| p < 0.86 | [ 0.950 0.005 -0.005 0.930 -0.002 0.500 ] |
| p < 0.93 | [ 0.035 -0.200 0.160 0.040 -0.090 0.020 ] |
| p < 1.00 | [ -0.040 0.200 0.160 0.040 0.083 0.120 ] |
Time (mean ± σ): 572.3 ms ± 8.5 ms [User: 533.0 ms, System: 31.7 ms]
Range (min … max): 562.6 ms … 590.9 ms 10 runs
Sierpinski Carpet
Parameters
| Generator (xn) | xn = xx * x + xy * y + xc (see below) |
| Generator (yn) | yn = yx * x + yy * y + yc (see below) |
| inside color | 128 |
| max iterations | 10000000 |
| parameter file | sierpinski-carpet |
| palette | sand |
| source | IteratedFunctionSystem.hpp |
Generator
| Probability | Transformation [ xx xy yx yy xc yc ] |
|---|---|
| p < 0.125 | [ 0.33 0.00 0.00 0.33 -0.66 0.66 ] |
| p < 0.250 | [ 0.33 0.00 0.00 0.33 0.00 0.66 ] |
| p < 0.375 | [ 0.33 0.00 0.00 0.33 0.66 0.66 ] |
| p < 0.500 | [ 0.33 0.00 0.00 0.33 -0.66 0.00 ] |
| p < 0.625 | [ 0.33 0.00 0.00 0.33 0.66 0.00 ] |
| p < 0.750 | [ 0.33 0.00 0.00 0.33 -0.66 -0.66 ] |
| p < 0.875 | [ 0.33 0.00 0.00 0.33 0.00 -0.66 ] |
| p < 1.000 | [ 0.33 0.00 0.00 0.33 0.66 -0.66 ] |
Time (mean ± σ): 429.3 ms ± 31.5 ms [User: 402.7 ms, System: 18.1 ms]
Range (min … max): 393.0 ms … 472.3 ms 10 runs
Sierpinski Triangle
Parameters
| Generator (xn) | xn = xx * x + xy * y + xc (see below) |
| Generator (yn) | yn = yx * x + yy * y + yc (see below) |
| inside color | 128 |
| max iterations | 10000000 |
| parameter file | sierpinski-triangle |
| palette | inverted gnpu |
| source | IteratedFunctionSystem.hpp |
Generator
| Probability | Transformation [ xx xy yx yy xc yc ] |
|---|---|
| p < 0.33 | [ 0.50 0.00 0.00 0.50 -0.50 -0.50 ] |
| p < 0.66 | [ 0.50 0.00 0.00 0.50 0.00 0.50 ] |
| p < 1.00 | [ 0.50 0.00 0.00 0.50 0.50 -0.50 ] |
Time (mean ± σ): 377.3 ms ± 26.8 ms [User: 353.2 ms, System: 16.8 ms]
Range (min … max): 350.7 ms … 432.0 ms 10 runs
Other Examples
Tree
Parameters: tree
Seaweed
Parameters: seaweed
Julia (Dragon)
Parameters: julia-dragon
Julia (Siegel Disk)
Parameters: julia-siegel
Julia (Flower)
Parameters: julia-flower
Mandelbrot (Histogram coloring)
Parameters: mandelbrot-histogram
Chrysantemum (Julia)
Parameters: chrysantemum
Cross Snowflakes
Parameters: cross-snowflakes
Crystal
Parameters: crystal
Dendrite (Julia)
Parameters: dendrite
EKG (Julia)
Parameters: ekg
Snowflakes (Julia)
Parameters: julia-snowflakes
Sine (Julia)
Parameters: julia-sin
Cosine (Julia)
Parameters: julia-cos
Dragon Curve
Parameters: dragon-curve
Julia (1/z|Conjugate)
Parameters: julia-funcs
Julia (c * fn(z))
Parameters: julia-func
Julia 6
Parameters: julia6
Koch Curve
Parameters: koch
Koch Triangle
Parameters: koch-triangle
Koch (Mix)
Parameters: kochmix
Leaf
Parameters: leaf
Leaf 2
Parameters: leaf2
Levy Curve
Parameters: levy-curve
Mandelbrot (Sine)
Parameters: mandelbrot-func
Mandelbrot (Sqr|Cos)
Parameters: mandelbrot-funcs
Mandelbrot (1/z^4)
Parameters: mandelbrot-reciprocal
Maple
Parameters: maple
Pascal Hadamard
Parameters: pascal-hadamard
Pentagon
Parameters: pentagon
Mandelbrot sinh^2(z)
Parameters: sinh
Snowflakes
Parameters: snowflakes
Tree 2
Parameters: tree2
Newton
Parameters: newton
Newton IV
Parameters: newton4
Barnsley Tree
Parameters: barnsleytree
Biomorphs
Biomorph M (Mandelbrot)
Parameters: biomorph-mandelbrot
Biomorph 1 (Julia)
Parameters: biomorph-julia
Biomorph 2 (Julia)
Parameters: biomorph-julia2
Biomorph 3 (Julia)
Parameters: biomorph-julia3
Biomorph 4 (Julia)
Parameters: biomorph-julia3
Biomorph 5 (Julia)
Parameters: biomorph-julia5
Biomorph 6 (Julia)
Parameters: biomorph-julia6
Biomorph 7 (Julia)
Parameters: biomorph-julia7
Biomorph 8 (Julia)
Parameters: biomorph-julia8