Önhasonlóság

Önhasonlóság, often translated as self-similarity, is a property of an object or phenomenon that appears the same or very similar at different scales. This means that if you zoom in on a part of the object, you will see a smaller version of the whole. This characteristic is fundamental to fractal geometry.

Objects exhibiting self-similarity can be perfectly self-similar, where the copies are exact replicas, or statistically self-similar, where the copies have the same statistical properties. Natural phenomena often display statistical self-similarity, such as coastlines, clouds, and branching patterns in trees. Mathematical fractals, like the Mandelbrot set or the Sierpinski triangle, are examples of perfectly self-similar objects.

The concept of self-similarity is crucial in understanding complex systems and patterns that are found throughout nature and in various scientific disciplines, including physics, biology, and computer science. It allows for the creation of intricate and irregular shapes using simple, repetitive rules. The study of önhasonlóság helps in modeling and analyzing complex structures that would otherwise be difficult to describe with traditional Euclidean geometry.