Kochhullámvonal

Kochhullámvonal is a Hungarian term that translates to "Koch wave" or "Koch curve." It refers to a specific type of fractal curve known for its self-similar properties. This fractal is generated through an iterative process. The construction typically begins with a simple line segment. In each subsequent step, the middle third of every line segment is replaced by two segments of the same length, forming an equilateral triangle pointing outward. This process is repeated infinitely, creating a curve with intricate detail at all scales.

The Koch curve exhibits a fractal dimension, which is a measure of its complexity and space-filling capacity. For the standard Koch curve, this dimension is approximately 1.2618. This means it is more complex than a simple line (dimension 1) but does not completely fill a two-dimensional space (dimension 2). The perimeter of a Koch curve is infinitely long, even though it encloses a finite area. This paradoxical property is characteristic of many fractals. The Koch curve is a visual example used in mathematics and computer graphics to demonstrate the principles of fractal geometry and recursive algorithms. It's a foundational example within the study of fractals.