Fractals are objects in which the same patterns occur again and again at different scales and sizes. In a perfect mathematical fractal – such as the famous Mandelbrot set, shown above – this “self-similarity” goes infinitely deep: each pattern is made up of smaller copies of itself, and those smaller copies are made up of smaller copies again, forever.

Many natural phenomena are fractal to some degree. Below are images of some of the most striking.


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Credit: Paul Oomen / Getty

The network of veins that move fluids around inside a leaf shows clear fractal structure. The circulatory system of animals is similar.


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Credit: Ian Cuming / Getty

The sixfold symmetry of this snowflake, due to the microscopic crystal structure of ice, is repeated several times. The central hexagon sprouts six more rough hexagons, and the outer corners of those produce still more hexagonal outgrowths.


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This image produced by high-voltage electricity discharging through a non-conductive material, known as a Lichtenberg figure, shows repetitive self-similar branching characteristic of a fractal.


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Credit: Fuhito Kanayama / Getty

Known as Romanesco cauliflower, Romanesco broccoli or even brocciflower, this relative of more common brassicas has a strikingly fractal appearance. The self-similar conical protrusions are composed of spiral on spiral of tiny buds.


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Credit: David Clapp / Getty

Braided glacial river channels in the southern Alps of New Zealand show large and small scale branching and recombination.


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Credit: Berndt Fischer / Getty

In many trees, such as this sycamore, a central trunk forks into two or more branches which themselves fork again and again into thinner and thinner branches before finally terminating in tiny twigs. Seven or more levels of branching can be counted in this image.