What are Fractals?

Overview:

Physicists use the fractal geometry approach to study quantum systems.

• A fractal is a never-ending pattern.
• Fractals are infinitely complex patterns that are self-similar across different scales.
• In essence, a fractal is a pattern that repeats forever, and every part of the fractal, regardless of how zoomed in or zoomed out you are, it looks very similar to the whole image.
• They are created by repeating a simple process over and over in an ongoing feedback loop.
• Driven by recursion, fractals are images of dynamic systems.
• Fractals are distinct from the simple figures of classical, or Euclidean, geometry—the square, the circle, the sphere, and so forth.
• Fractal patterns are extremely familiar, since nature is full of fractals. For instance, trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc.
• They are capable of describing many irregularly shaped objects or spatially nonuniform phenomena in nature, such as coastlines and mountain ranges.
• Applications: Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.

Q1) What is Euclidean geometry?

Euclidean geometry is a branch of geometry that originated from the works of the ancient Greek mathematician Euclid. It is based on a set of axioms and postulates, forming the foundation for classical geometry.