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.

self-similar patterns

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

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.

patterns that repeat at increasingly fine magnifications

Fractals are patterns that repeat at increasingly fine magnifications.

objects with irregular curves or shapes

Fractals are objects with irregular curves or shapes and are recognizable building blocks of nature.

never-ending patterns made by repeating the same idea over again

Fractals are never-ending patterns made by repeating the same idea over again.

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.

images of dynamic systems - the pictures of Chaos

Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos.

mathematical characterisations of self-repeating patterns often described as the 'fingerprints of nature

Fractals are mathematical characterisations of self-repeating patterns often described as the 'fingerprints of nature'.

images of dynamic systems that are driven by recursion

Fractals are images of dynamic systems that are driven by recursion.

never-ending patterns that look the same whether analyzed from near or far

Fractals are never-ending patterns that look the same whether analyzed from near or far, since each part of these geometric figures has a similar character as the whole.

never-ending patterns that can be found all over the natural world (for instance in tree branches, rivers, blood vessels, sea shells, hurricanes, galaxies, etc) and they can also be made with a computer using simple algebraic equations.

Fractals are never-ending patterns that can be found all over the natural world (for instance in tree branches, rivers, blood vessels, sea shells, hurricanes, galaxies, etc) and they can also be made with a computer using simple algebraic equations.

beautiful, never-ending patterns , that are found in nature

Fractals are beautiful, never-ending patterns that are found in nature, consisting of subsets that are similar to each other and to the parent pattern.

beautiful, never-ending patterns that are found in nature, consisting of subsets that are similar to each other and to the parent pattern

Fractals are beautiful, never-ending patterns that are found in nature, consisting of subsets that are similar to each other and to the parent pattern.

never-ending patterns, mathematical formulas that reveal nature's blueprint

Fractals are never-ending patterns, mathematical formulas that reveal nature's blueprint.