Starting at {0,0} along the axis, move several unit steps, rotating 90° before each step:

A polyline of three segments:

Advance 20 steps, always turning 110° toward the left:

Generate the transformation functions of a path:

Apply them to a turtle:

Use symbolic input:

Make a random walk where successive steps change direction by at most 20°:

Generate a dragon curve:

Generate a Koch snowflake curve:

Another pattern based on the Thue–Morse sequence:

Angles are accumulated in subsequent steps, starting with θ₀:

These two results are identical:

Take 100 random angles between and :

Considered as absolute angles, they represent on average a collection of steps toward the right:

Considered as relative angles, the path may evolve in any possible direction. The total length is the same:

Global frame rotations can be obtained as multiplications of all previous relative rotations:

Compute the positions for a path with the following inputs:

Each new position can be computed as a displacement along a rotation of the initial x axis:

When using the notation {{x,y},{dx,dy}} for the first argument, {dx,dy} determines the initial orientation, not the position of the next point:

Move the turtle by steps of given length and relative direction:

Draw lines for which each segment forms a uniformly increasing angle with the previous segment:

Draw lines for which consecutive relative angles increase by 1 radian:

Draw a line for which consecutive relative angles increase and are modulated by a Sin function:

Add color to the individual segments of the angle path: