A Journey Beyond Traditional Geometry with Fractals
Fractals are intricate shapes that replicate their patterns at every scale. Imagine a shape that, when zoomed in on, reveals layers of similar patterns, each a smaller version of the whole. In this article, we’ll explore the math that defines fractals, how fractals relate to evolution, and we’ll dive into some visual examples using Python and JavaScript.
Chapter 1: Fractals Defined
A fractal is a complex pattern where each part has the same statistical character as the whole. They are generally self-similar (patterns that repeat themselves at different scales).
Key Properties:
- Self-Similarity: Smaller portions of the fractal resemble the whole.
- Infinite Complexity: Fractals look detailed at any scale.
- Fractional Dimension: Fractals exist between our traditional dimensions.
Fractal Mathematics: Mandelbrot and Sierpinski
The concept of fractals was formalized by Benoit Mandelbrot in the 1970s. Mandelbrot’s work, particularly his book “The Fractal Geometry of Nature,” revolutionized the way we understand complex geometric shapes.
Mandelbrot Set: Named after Benoit Mandelbrot, the Mandelbrot set is formed by…
