Hypocycloid prove that an epicycloid with "k" cusps moves snugly inside one with "k"+1 cusps. The evolute of a hypocycloid is an enlarged version of the hypocycloid itself, while the involute of a hypocycloid is a reduced copy of itself. The pedal of a hypocycloid with pole at the center of the hypocycloid is a rose curve. The isoptic of a hypocycloid is a hypocycloid. Curves similar to hypocyloids can be drawn with the Spirograph toy. Specifically, the Spirograph can draw hypotrochoids and epitrochoids. The Pittsburgh Steelers' logo, which is based on the Steelmark, includes three astroids (hypocycloids of four cusps).
Fisher's geometric model by small mutations. Furthermore, Orr discovered that both the fixation probability of a beneficial mutation and the fitness gain that is conferred by the fixation of the beneficial mutation decrease with organismal complexity. Thus, the predicted rate of adaptation decreases quickly with the rise in organismal complexity, a theoretical finding known as the ‘cost of complexity’. Fisher's geometric model Fisher's geometric model (FGM) is an evolutionary model of the effect sizes and effect on fitness of spontaneous mutations proposed by Ronald Fisher to explain the distribution of effects of mutations that could contribute to adaptative evolution. Sometimes referred to as