Examples for

# 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:

Nowhere-Differentiable Functions

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

#### Evaluate a nowhere-differentiable function at a point:

Fractals in 3D

Examine fractal behavior in three dimensions.

#### Draw the Menger sponge:

Shape-Replacement Fractals

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

#### Draw fractals by repeatedly adding smaller figures:

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Space-Filling Curves

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

#### Specify the number of iterations to use:

Other Fractals

Explore various types of fractals.

### RELATED EXAMPLES

• Applied Mathematics
• Computational Sciences
• Geometry
• Substitution Systems
• Wolfram Language
• Mandelbrot & Julia Sets

Compute and visualize Mandelbrot and associated Julia sets.

#### Plot the Multibrot set of exponent d:

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