Explore the Depths of the Mandelbrot Set
This tool generates a part of the Mandelbrot Set fractal every few seconds. The Mandelbrot Set is one of the most iconic and mysterious fractals in mathematics, discovered by Benoît B. Mandelbrot in the late 20th century.
This fractal is generated from a deceptively simple formula, yet it reveals literally endless layers of complexity and beauty. The Mandelbrot Set is more than just a visual marvel: it represents the boundary between stability and chaos in complex systems and is a mathematical gateway into understanding fractals and recursive structures in nature.
The project above dynamically renders random sections of the Mandelbrot Set at different levels of magnification, letting you experience unique regions of this fractal universe with stunning, customizable color schemes. Each scene is computed in real time in the browser, and highlights the intricate, self-repeating patterns that define fractals.
The Math Behind the Mandelbrot Set The Mandelbrot Set is defined by iterating the following equation for each point 𝑐 in the complex plane:
Where:
- 𝑧 starts at 0 for each point,
- 𝑐 is the complex coordinate of the point on the plane,
- The point 𝑐 c is considered part of the Mandelbrot Set if the sequence does not diverge to infinity after a large number of iterations.
In practice, we check if ∣𝑧∣ exceeds 2 after a set number of iterations to determine if it "escapes" the set. Those points that stay bounded within this limit create the iconic "bulbs and tendrils" of the Mandelbrot Set, while those that escape reveal the colorful edges around it. This project above tries to make sure to find interesting locations instead of zooming in on empty parts of the fractal.
Customize your experience with different color schemes and animation timing as you explore random fractals with this captivating intersection of art and mathematics!
