Epitrochoid and Hypotrochoid Animation Gallery

spirograph spiralGraph
A hypotrochoid {1,6/13,h} with parameter h varing from .15 to 1.3. Each image is scaled so they all fit the display boundary.
spirograph flashingIllusion
A illusion created by superimposing two hypotrochoids {1,1/7,2} rotating in opposite direction.
spirograph snowFlake1 spirograph snowFlake2
“Snowflake”. Based on catacaustic of a changing epitrochoid {1,1/6,h} with light source at the center. The one on the right shows detail at the center.
flashingDiamond flashingDiamond
“Flashing Diamond” based on evolute of ahypotrochoid with varing parameter h. {1,1/4,h}
superNova superNova
“SuperNova” based on evolute of ahypotrochoid with varing parameter h. {1,3/7,h}
inverseRose inverseRose
“Rose and Cotes' spiral”. Inverse of a quadrifolium {1, 1/4, 3/4} with respect to its center, and increasing radius of inversion. The resulting curve is a Cotes' spiral. (the red dots)

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