Locus of line segments

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If we take a line segment of infinitesimally small length, and draw another line segment of the same length from the endpoint of the first at a particular angle and repeat this infinite number of times, what shape will we get? I think we might get a circle in one case and various spirals in the rest, depending on the angle, but I am not sure.

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If the angle is found in any regular polygon, i.e., is of the type

$$\frac{180^\circ(n-2)}n$$

then it will form an $n$-sided regular polygon, else it will form a spiral. This will intersect itself if the angle is less than $60^\circ$, and will form a circle as it approaches $180^\circ$.