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.

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

#### Draw a fractal based on iterated line replacement:

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:

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:

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:

Explore various types of fractals.

#### Plot a curlicue fractal:

### RELATED EXAMPLES

Compute and visualize Mandelbrot and associated Julia sets.