Fractal: the whole of a disjointed picture

A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. If the replication is exactly the same at every scale, it is called a self-similar pattern.

Architecture has traditionally used Euclidean geometry that represents pure volumes that can be defined by equations. It enables us to describe smooth surfaces and regular forms. However, natural objects such as mountains have irregular, fragmented characteristics.

Fractal Geometry in the Sagrada Familia | nave detail

Natural models can be described realistically by using methods of fractal geometry, using procedures and equations. A fractal object has two basic characteristics: infinite detail at each point and a degree of self-similarity between the parts of the object and its overall characteristics.

The Cube | Fractal in architectural design

Processes to represent the object viewed from different distances, with the same degree of detail. Fractal methods have shown themselves to be useful in moulding terrains, clouds, water, trees and other plants. Fractal patterns have been identified in the behaviour of stars, meanders, stock-market variations, traffic flows, the use of the urban property.

fractals in the design of the Eiffel Tower