What are fractal patterns?

Fractal patterns are geometric shapes that can be split into parts, each of which is a reduced-scale copy of the whole. This self-similarity is a key characteristic of fractals.

Properties of fractal patterns:

Self-similarity: A fractal pattern looks similar at various scales.
Fine structure: Fractals exhibit intricate, detailed patterns at all scales.
Non-integer dimension: Fractals can have a dimension that is not a whole number, indicating their complex and irregular nature.
Infinite complexity: Fractal patterns can be infinitely complex, with detail at every level of magnification.

Examples of fractal patterns in nature:

Coastlines
Snowflakes
Mountain ranges
Clouds
Lightning bolts
Broccoli and cauliflower

Mathematical representation of fractal patterns:

Fractal patterns can be created using mathematical equations such as the Mandelbrot set, Julia set, and Koch curve. These equations involve iterative processes that create self-similar patterns.

Applications of fractal patterns:

Art and design: Fractals are used to create visually stunning, intricate designs in art and architecture.
Compression algorithms: Fractal compression is a method used to compress images and signals while preserving fine details.
Computer graphics: Fractal patterns are used to generate realistic textures and landscapes in computer-generated imagery.
Modeling natural phenomena: Fractals are used to model irregular natural phenomena, such as the shape of coastlines and the growth of plants.