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# Fractals

A fractal is an object or quantity that exhibits self-similarity on all scales. Use Wolfram|Alpha to explore a vast collection of fractals and to visualize beautiful chaotic and regular behaviors. Examine named fractals, visualize iteration rules, compute fractal dimension and more.

Line-Replacement Fractals

Compute properties regarding fractals created by repeatedly applying iteration rules on curves.

Draw a fractal based on iterated line replacement:

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Nowhere-Differentiable Functions

Ask about continuous functions that are nowhere differentiable or ask for the value at a particular point.

Plot an approximation to a nowhere-differentiable function:

Evaluate a nowhere-differentiable function at a point:

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Space-Filling Curves

Perform various iterations whose limiting behaviors lead to space-filling curves.

Plot an approximation to a space-filling curve:

Specify the number of iterations to use:

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Fractals in 3D

Examine fractal behavior in three dimensions.

Draw the Sierpinski tetrahedron:

Draw the Menger sponge:

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Other Fractals

Explore various types of fractals.

Plot a curlicue fractal:

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