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

• [1] M. McGuire: https://www.shadertoy.com/view/4dS3Wd
• [2] I. Quilez: https://iquilezles.org/articles/fbm
• [3] P. Gonzalez-Vivo & J. Lowe: https://thebookofshaders.com/13
• [4] SVGStorm: https://svgstorm.com/app
• [5] Inkscape: https://inkscape.org