patterns that are self-similar on different scales

Fractals are patterns that are self-similar on different scales, and they can occur quite naturally.

self-similar

Fractals are infinitely complex patterns that are self-similar across different scales.

patterns that self-repeat at different scales

Fractals are patterns that self-repeat at different scales, and they can be found all over nature in objects like trees, rivers, clouds and coastlines.

an object that displays self-similarity

A fractal is an object that displays self-similarity.

geometric patterns

Fractals are geometric patterns which can often be generated procedurally.

self-similar patterns, where self-similar means they are the same from near as from far Fractals

The mathematical definition of a fractal also says something similar: Fractals are typically self-similar patterns, where self-similar means they are the same from near as from far Fractals may be the same at every scale.

shapes that repeat themselves on smaller and smaller scales

Fractals are shapes that repeat themselves on smaller and smaller scales, and they’re something that mathematicians study, though the ones on romanesco broccoli aren’t true fractals because nothing on earth is exactly a fractal.

self-similar patterns that can be found throughout the natural world, but are uncommon in human-made structures (Mandelbrot, 1983)

Fractals are self-similar patterns that can be found throughout the natural world, but are uncommon in human-made structures (Mandelbrot, 1983).

complex patterns

Fractals are complex patterns but they are actually made by repeating a simple process.

complex geometric patterns with a self-similar structure

Fractals are complex geometric patterns with a self-similar structure -

self-similar complex patterns that are created by repeating a simple process over and over in an ongoing feedback loop

Fractals are self-similar complex patterns that are created by repeating a simple process over and over in an ongoing feedback loop.

a kind of shape that can be split into parts

A fractal is a kind of shape that can be split into parts, each of which approximates the whole.

self-similar structure like the above triangle, in which the parts are similar to the whole (in this case exactly half the scale as parent triangle)

Fractals are self-similar structure like the above triangle, in which the parts are similar to the whole (in this case exactly half the scale as parent triangle).

mathematical sets that show self-similar patterns

Fractals are mathematical sets that show self-similar patterns: zoom in on one part of a fractal drawing, such as the famous Mandelbrot set, and the smaller portion will look nearly the same as the original image.

a mathematical set displaying self-similar patterns

Officially, a fractal is a mathematical set displaying self-similar patterns.

which contain within them self-similar patterns in varying degrees of time or size

Fractals are patterns which contain within them self-similar patterns in varying degrees of time or size.

self-similar patterns that repeat at all scales and provide a more dynamic and nuanced understanding of market structure

Fractals are self-similar patterns that repeat at all scales and provide a more dynamic and nuanced understanding of market structure.

self-similar infinitely repeating patterns created using simple recursive math equations

Fractals are self-similar infinitely repeating patterns created using simple recursive math equations.

mathematical self-similar structures that help in analyzing the crypto market

Fractals are mathematical self-similar structures that help in analyzing the crypto market.

self-similar (bits look like the whole) and independent of scale (they look similar, no matter how close you zoom in)

Fractals are generally self-similar (bits look like the whole) and independent of scale (they look similar, no matter how close you zoom in).