n cusps
n = 2 · diameter
degenerate · line across circle
Deltoid n = 3
3 cusps · 3-fold symmetry
Astroid n = 4
x⅓˳ + y⅓˳ = R⅓˳ · 4-cusp
n = 5
5 cusps · pentacycloid
n = 7
7 cusps · prime
n = 10
10 cusps · 10-fold star
n = 15
15 cusps · fine ring
n = 20
20 cusps · dense ring
Cusps n
4
Color
★ Accent
🌈 Orbit
❖ Per cusp
Speed
▶ Slow
▶▶ Normal
▶▶▶ Fast
⊙ Mechanism
Pen on rim, rolling INSIDE.
Cusps touch the outer circle.
n = 2: degenerate diameter.
n = 4: x²˳ + y²˳ = R²˳.
n =
4
cusps =
4
k = r/R =
1/4
θ =
0.000
x²˳ + y²˳ = R²˳
Presets
— choose cusp count
n slider
— morph 2 → 24
Per cusp
— one hue per cusp