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.

#### Plot an approximation to a nowhere-differentiable function:

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

### Fractals in 3D

Examine fractal behavior in three dimensions.

#### Draw the Sierpinski tetrahedron:

#### Draw the Menger sponge:

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

#### Draw fractals based on replacement of shapes:

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

### 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:

### Other Fractals

Explore various types of fractals.

#### Plot a curlicue fractal:

### RELATED EXAMPLES

Compute and visualize Mandelbrot and associated Julia sets.