Dilatación y giro de la espiral equiangular

"This curve was first recognized by Descartes. Jacob Bernouilli found it so fascinating that he arranged to have it engraved on his tombstone with the inscription

These words ("Though changed I shall arise the same") express a remarkable consequence of the way the curve can be shifted along itself by a dilative rotation: any dilatation has the same effect on it as a rotation, and vice versa." (Coxeter)