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.

self-similar mathematical objects, where the similarities occur at different sizes

Fractals are self-similar mathematical objects, where the similarities occur at different sizes.

patterns that repeat at increasingly fine magnifications

Fractals are patterns that repeat at increasingly fine magnifications.

never-ending patterns that tend to be infinitely complex that also tend to be self-similar at different scales

Fractals are never-ending patterns that tend to be infinitely complex that also tend to be self-similar at different scales.

self-similar

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

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

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

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.

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).

self-similar objects (), which look the same at all scaleswhose dimensions can be noninteger

Fractals are self-similar objects (which look the same at all scales), whose dimensions can be noninteger.

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

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

self-similar objects with non integer dimension

Fractals are self-similar objects with non integer dimension; they are also important to determine the macroscopic properties of the system by microscopic dynamics of system, which has been an area of scientific interest for a long time.

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).