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There''s more than one. First they are easiest to wrote down in polar coordinates, e.g. r = f(t), where r is the radius or distance from the origin and t is the angle rotated through.

In this form the two most common spirals have equations

r = a * t

r = a * b^t

The first equation gives you a spiral with a constant gap as the spiral expands. This is the spiral you get when you wrap or roll up into a spiral. E.g. a roll of paper, or a spiral of string glued onto card.

The second spiral gives you an equal angled spiral, and is the same as seen in spiral shells and other self-similar spiral forms in nature.

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