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Fractal Image Generators in SDL
https://github.com/daelsepara/sdl-fractals
biomorph biomorphs escape-time-algorithm fractal-algorithms fractals mandelbrot sdl sdl2
Last synced: 1 day ago
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Fractal Image Generators in SDL
Host: GitHub
URL: https://github.com/daelsepara/sdl-fractals
Owner: daelsepara
License: gpl-3.0
Created: 2023-09-22T14:21:15.000Z (over 1 year ago)
Default Branch: main
Last Pushed: 2025-02-02T14:47:10.000Z (18 days ago)
Last Synced: 2025-02-02T15:31:49.061Z (18 days ago)
Topics: biomorph, biomorphs, escape-time-algorithm, fractal-algorithms, fractals, mandelbrot, sdl, sdl2
Language: C++
Homepage: https://daelsepara.github.io/sdl-fractals/
Size: 34.7 MB
Stars: 1
Watchers: 1
Forks: 0
Open Issues: 0
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project

README

        Fractal Image Generators in SDL

# GitHub Repository

[https://github.com/daelsepara/sdl-fractals](https://github.com/daelsepara/sdl-fractals)

# Building (Unix/Linux)

```cmd

cd repository/src

make

```

**Dependencies**: sdl2, sdl2-image

# Usage

```cmd

./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/](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/) for sample parameter files.

## Optional parameters

#### /IMAGE={image.png}

Save fractal to *{image.png}*

#### /PALETTE={palette.json}

Use *{palette.json}* colormap. See [palettes/](https://github.com/daelsepara/sdl-fractals/tree/main/src/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

![Mandelbrot Set](samples/mandelbrot.png)

### Parameters

|||

|---------------|-----------------------|

|Generator      | **z**^**exp** + **C** |

|exponent       | 2 |

|max iterations | 255 |

|escape value   | 4.0 |

|parameter files| [mandelbrot](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/mandelbrot.json), [mandelbrot2](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/mandelbrot2.json), [mandelbrot3](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/mandelbrot3.json) |

|palette        | default |

|source(s)      | [Mandelbrot.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Mandelbrot.hpp), [Mandelbrot2.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Mandelbrot2.hpp), [Mandelbrot3.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Mandelbrot3.hpp) |

### Benchmarks

**mandelbrot**

```cmd

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**

```cmd

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**

```cmd

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

![Newton](samples/newton1.png)

### Parameters

|||

|---------------|----------------------------------|

|Generator      | **z** - (**z**^3 - 1)/(3**z**^2) |

|tolerance      | 1e-6 |

|max iterations | 255 |

|parameter file | [newton1](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/newton1.json) |

|palette        | default |

|source         | [Newton1.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Newton1.hpp) |

```cmd

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](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Julia.hpp) |

### Specific Parameters and Benchmarks

![Julia 1](samples/julia1.png)

|||

|----------|-------------|

|C         | -0.4 + 0.6i |

|parameter file| [julia1](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia1.json) |

|palette   | [magma](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/magma.json) |

```cmd

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

```

![Julia 2](samples/julia2.png)

|||

|----------|---------------|

|C         | -0.8 + 0.156i |

|parameter file| [julia2](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia2.json) |

|palette   | [inferno](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/inferno.json) |

```cmd

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

```

![Julia 3](samples/julia3.png)

|||

|----------|---------------|

|C         | 0.285 + 0.01i |

|parameter file| [julia3](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia3.json) |

|palette   | [moreland](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/moreland.json) |

```cmd

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

```

![Julia 4](samples/julia4.png)

|||

|----------|-------------------|

|C         | -0.7269 + 0.1889i |

|parameter file| [julia4](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia4.json) |

|palette   | [magma](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/magma.json) |

```cmd

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

```

![Julia 5](samples/julia5.png)

|||

|----------|-------------------|

|C         | 0.26294324588 - 0.0024215732998i |

|max iterations | 320 |

|normalized colormap | true |

|parameter file| [julia5](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia5.json) |

|palette   | inverted [jet](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/jet.json) |

```cmd

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

![Mandelbrot 4](samples/mandelbrot4.png)

### Parameters

|||

|---------------|-----------------------|

|Generator      | **z**^**exp** + **C** |

|exponent       | 4 |

|max iterations | 255 |

|escape value   | 4.0 |

|parameter file | [mandelbrot4](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/mandelbrot4.json) |

|palette        | default |

|source         | [Mandelbrot.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Mandelbrot.hpp) |

```cmd

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

![Burning Ship](samples/burningship.png)

### 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](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/burningship.json) |

|palette        | [hot](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/hot.json) |

|source         | [Mandelbrot.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Mandelbrot.hpp) |

```cmd

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)

![Burning Ship 2](samples/burningship2.png)

### 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](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/burningship2.json) |

|palette        | [plasma](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/plasma.json) |

|source         | [Mandelbrot.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Mandelbrot.hpp) |

```cmd

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)

![Burning Ship 3](samples/burningship3.png)

### 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](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/burningship2.json) |

|palette        | [bluered](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/bluered.json) |

|source         | [Mandelbrot.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Mandelbrot.hpp) |

```cmd

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

![Tricorn](samples/tricorn.png)

### 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](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/tricorn.json) |

|palette        | [parula](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/parula.json) |

|source         | [Tricorn.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Tricorn.hpp) |

```cmd

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

![Multicorn](samples/multicorn.png)

### Parameters

|||

|---------------|---------------------------|

|Generator      | **Z_bar**^**exp** + **C** |

|exponent       | 4 |

|inside color   | 0 |

|max iterations | 255 |

|escape value   | 4.0 |

|parameter file | [multicorn](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/multicorn.json) |

|palette        | [viridis](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/viridis.json) |

|source         | [Mandelbrot.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/Mandelbrot.hpp) |

```cmd

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

![Barnsley Fern](samples/barnsleyfern.png)

### 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](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/barnsleyfern.json) |

|palette        | [green](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/green.json) |

|source         | [IteratedFunctionSystem.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/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 ]  |

```cmd

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)

![Barnsley Fern](samples/culcita.png)

### 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](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/culcita.json) |

|palette        | [green](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/green.json) |

|source         | [IteratedFunctionSystem.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/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 ]  |

```cmd

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)

![Barnsley Fern](samples/thelypteridaceae.png)

### 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](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/thelypteridaceae.json) |

|palette        | [green](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/green.json) |

|source         | [IteratedFunctionSystem.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/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 ]  |

```cmd

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

![Sierpinski Carpet](samples/sierpinski-carpet.png)

### 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](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/sierpinski-carpet.json) |

|palette        | [sand](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/sand.json) |

|source         | [IteratedFunctionSystem.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/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  ] |

```cmd

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

![Sierpinski Triangle](samples/sierpinski-triangle.png)

### 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](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/sierpinski-triangle.json) |

|palette        | inverted [gnpu](https://github.com/daelsepara/sdl-fractals/tree/main/src/palettes/gnpu.json) |

|source         | [IteratedFunctionSystem.hpp](https://github.com/daelsepara/sdl-fractals/tree/main/src/fractals/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  ] |

```cmd

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

![Tree](samples/tree.png)

**Parameters:** [tree](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/tree.json)

## Seaweed

![Seaweed](samples/seaweed.png)

**Parameters:** [seaweed](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/seaweed.json)

## Julia (Dragon)

![Julia Dragon](samples/julia-dragon.png)

**Parameters:** [julia-dragon](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia-dragon.json)

## Julia (Siegel Disk)

![Julia Siegel Disk](samples/julia-siegel.png)

**Parameters:** [julia-siegel](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia-siegel.json)

## Julia (Flower)

![Julia Flower](samples/julia-flower.png)

**Parameters:** [julia-flower](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia-flower.json)

## Mandelbrot (Histogram coloring)

![Mandelbrot Histogram](samples/mandelbrot-histogram.png)

**Parameters:** [mandelbrot-histogram](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/mandelbrot-histogram.json)

## Chrysantemum (Julia)

![Chrysantemum](samples/chrysantemum.png)

**Parameters:** [chrysantemum](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/chrysantemum.json)

## Cross Snowflakes

![Cross Snowflakes](samples/cross-snowflakes.png)

**Parameters:** [cross-snowflakes](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/cross-snowflakes.json)

## Crystal

![Crystal](samples/crystal.png)

**Parameters:** [crystal](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/crystal.json)

## Dendrite (Julia)

![Dendrite](samples/dendrite.png)

**Parameters:** [dendrite](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/dendrite.json)

## EKG (Julia)

![EKG](samples/ekg.png)

**Parameters:** [ekg](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/ekg.json)

## Snowflakes (Julia)

![Snowflakes](samples/julia-snowflakes.png)

**Parameters:** [julia-snowflakes](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia-snowflakes.json)

## Sine (Julia)

![Sine](samples/julia-sin.png)

**Parameters:** [julia-sin](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia-sin.json)

## Cosine (Julia)

![Cosine](samples/julia-cos.png)

**Parameters:** [julia-cos](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia-cos.json)

## Dragon Curve

![Dragon Curve](samples/dragon-curve.png)

**Parameters:** [dragon-curve](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/dragon-curve.json)

## Julia (1/z|Conjugate)

![Julia (1/z|Conjugate)](samples/julia-funcs.png)

**Parameters:** [julia-funcs](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia-funcs.json)

## Julia (c * fn(z))

![Julia (c * fn(z)](samples/julia-func.png)

**Parameters:** [julia-func](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia-func.json)

## Julia 6

![Julia 6](samples/julia6.png)

**Parameters:** [julia6](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/julia6.json)

## Koch Curve

![Koch Curve](samples/koch.png)

**Parameters:** [koch](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/koch.json)

## Koch Triangle

![Koch Triangle](samples/koch-triangle.png)

**Parameters:** [koch-triangle](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/koch-triangle.json)

## Koch (Mix)

![Koch (Mix)](samples/kochmix.png)

**Parameters:** [kochmix](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/kochmix.json)

## Leaf

![Leaf](samples/leaf.png)

**Parameters:** [leaf](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/leaf.json)

## Leaf 2

![Leaf 2](samples/leaf2.png)

**Parameters:** [leaf2](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/leaf2.json)

## Levy Curve

![Levy Curve](samples/levy-curve.png)

**Parameters:** [levy-curve](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/levy-curve.json)

## Mandelbrot (Sine)

![Mandelbrot (Sine)](samples/mandelbrot-func.png)

**Parameters:** [mandelbrot-func](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/mandelbrot-func.json)

## Mandelbrot (Sqr|Cos)

![Mandelbrot (Sqr|Cos)](samples/mandelbrot-funcs.png)

**Parameters:** [mandelbrot-funcs](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/mandelbrot-funcs.json)

## Mandelbrot (1/z^4)

![Mandelbrot (1/z^4)](samples/mandelbrot-reciprocal.png)

**Parameters:** [mandelbrot-reciprocal](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/mandelbrot-reciprocal.json)

## Maple

![Maple](samples/maple.png)

**Parameters:** [maple](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/maple.json)

## Pascal Hadamard

![Maple](samples/pascal-hadamard.png)

**Parameters:** [pascal-hadamard](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/pascal-hadamard.json)

## Pentagon

![Pentagon](samples/pentagon.png)

**Parameters:** [pentagon](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/pentagon.json)

## Mandelbrot sinh^2(z)

![Mandelbrot sinh^2(z)](samples/sinh.png)

**Parameters:** [sinh](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/sinh.json)

## Snowflakes

![Snowflakes](samples/snowflakes.png)

**Parameters:** [snowflakes](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/snowflakes.json)

## Tree 2

![Tree2](samples/tree2.png)

**Parameters:** [tree2](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/tree2.json)

## Newton

![Newton](samples/newton.png)

**Parameters:** [newton](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/newton.json)

## Newton IV

![Newton IV](samples/newton4.png)

**Parameters:** [newton4](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/newton4.json)

## Barnsley Tree

![Barnsley Tree](samples/barnsleytree.png)

**Parameters:** [barnsleytree](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/barnsleytree.json)

# Biomorphs

## Biomorph M (Mandelbrot)

![Biomorph (Mandelbrot)](samples/biomorph-mandelbrot.png)

**Parameters:** [biomorph-mandelbrot](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/biomorph-mandelbrot.json)

## Biomorph 1 (Julia)

![Biomorph (Julia)](samples/biomorph-julia.png)

**Parameters:** [biomorph-julia](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/biomorph-julia.json)

## Biomorph 2 (Julia)

![Biomorph (Julia)](samples/biomorph-julia2.png)

**Parameters:** [biomorph-julia2](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/biomorph-julia2.json)

## Biomorph 3 (Julia)

![Biomorph (Julia)](samples/biomorph-julia3.png)

**Parameters:** [biomorph-julia3](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/biomorph-julia3.json)

## Biomorph 4 (Julia)

![Biomorph (Julia)](samples/biomorph-julia4.png)

**Parameters:** [biomorph-julia3](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/biomorph-julia4.json)

## Biomorph 5 (Julia)

![Biomorph (Julia)](samples/biomorph-julia5.png)

**Parameters:** [biomorph-julia5](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/biomorph-julia5.json)

## Biomorph 6 (Julia)

![Biomorph (Julia)](samples/biomorph-julia6.png)

**Parameters:** [biomorph-julia6](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/biomorph-julia6.json)

## Biomorph 7 (Julia)

![Biomorph (Julia)](samples/biomorph-julia7.png)

**Parameters:** [biomorph-julia7](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/biomorph-julia7.json)

## Biomorph 8 (Julia)

![Biomorph (Julia)](samples/biomorph-julia8.png)

**Parameters:** [biomorph-julia8](https://github.com/daelsepara/sdl-fractals/tree/main/src/parameters/biomorph-julia8.json)