In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension.

Mar 28, 2025 · Fractals are distinct from the simple figures of classical, or Euclidean, geometry—the square, the circle, the sphere, and so forth. They are capable of describing many irregularly shaped objects or spatially nonuniform phenomena in nature such as coastlines and mountain ranges.

Jan 29, 2024 · Fractal geometry deals with complexity and irregularity. While on the other hand, traditional Euclidean geometry, deals primarily with simple shapes such as circles, squares, and triangles. Types of fractals: Fractals have three basic types which are below. Self-similar fractals; Self-affine fractals; Invariant fractals; Now we explain all of ...

Oct 31, 2023 · Fractal geometry enables us to more accurately define and measure the complexity of a shape by quantifying how rough its surface is. You can express the jagged edges of that mountain mathematically. Advertisement

Fractals have detail at arbitrarily small scales and display irregularity that cannot be described by traditional geometrical language. In other words, fractals are objects which, at any magnification, will never “smooth out” to look like Euclidean space.

Sep 12, 2020 · Fractals are mathematical sets, usually obtained through recursion, that exhibit interesting dimensional properties. We’ll explore what that sentence means through the rest of this section. For now, we can begin with the idea of self-similarity, a characteristic of most fractals.

A tutorial on basic fractal geometry and a panorama of uses of fractals, with supporting software, laboratory exercises, and resources for teachers

What is a fractal? A rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole. A set of points whose fractal dimension exceeds its topological dimension. The classic Mandelbrot below has been the image that has greatly popularised chaotic and fractal systems.

1 day ago · The word fractal was first used in 1975 by Benoît Mandelbrot, a French-American mathematician, who described intricate shapes and patterns that repeat even when an object is viewed at different levels of scale. Mandelbrot defined a fractal as “a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least ...

Nov 26, 2024 · Imagine a shape so intricate that it reveals infinite complexity as you zoom in on a structure where patterns repeat endlessly at every scale. These mesmerizing forms, known as fractals, defy traditional geometric conventions and open a …