# Fractional Brownian Motion Generator

Version 1.0.0 (6.59 MB) by
Generate patterns using the fractional Brownian motion
Updated 26 Apr 2023

# Fractional Brownian Motion (FBM) Generator

This code generates patterns using the fractional Brownian motion (FBM), a mathematical technique used to create fractal-like images. The code is inspired in the well-documented posts from M. McGuire [1], I. Quilez [2], and P. Gonzalez-Vivo & J. Lowe [3].

The code was used to create the cover of my PhD thesis titled `Development of a wide-spectrum thermochemical code with application to planar reacting and non-reacting shocks`.

The process to generate the cover was as follows:

1. Get an image that mimics turbulence using the script.
2. Vectorize the image using SVGStorm [4]. This will homogenize the image without the need to generate a large image.
3. Post-process the image using Inkscape [5].

# Preview

## Usage

The function can be called with optional name-pair arguments, such as:

• zoom (float): Zoom factor of the image.
• octaves (float): Number of octaves.
• resolution (float): Resolution of the image (width, height) in pixels.
• palette (float): Colormap of the image, e.g., `summer` or `winter`.
• ntimes (float): Number of images to generate.
• velocity (float): Velocity of the pattern.
• direction (float): Direction of the pattern (x, y).

## Examples:

```fbm()
fbm('resolution', [640, 360])
fbm('resolution', [640, 360], 'zoom', 0.5)
fbm('resolution', [640, 360], 'zoom', 0.5, 'octaves', 4)
fbm('resolution', [640, 360], 'zoom', 0.5, 'octaves', 4, 'ntimes', 1000)
fbm('resolution', [640, 360], 'zoom', 0.5, 'octaves', 4, 'ntimes', 1000, 'velocity', 5)
fbm('resolution', [640, 360], 'zoom', 0.5, 'octaves', 4, 'ntimes', 1000, 'velocity', 5, 'palette', 'winter')```

## References

### Cite As

Alberto Cuadra Lara (2024). Fractional Brownian Motion Generator (https://github.com/AlbertoCuadra/fbm/releases/tag/v1.0.0), GitHub. Retrieved .

##### MATLAB Release Compatibility
Created with R2023a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.0.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.