Cissoid Art Animations
Mathematical beauty in motion – Exploring the artistic side of the Cissoid curve
🌀 Spinning Cissoid
Rotating cissoid with particle trail effects
✨ Particle Resonance
Particles following cissoid paths
🌊 Wave Cissoid
Interference patterns forming cissoids
🎭 Kaleidoscopic Cissoid
Symmetrical reflections and patterns
🌿 Organic Cissoid
Natural growth patterns inspired by cissoids
💫 Neon Cissoid
Glowing network of interconnected cissoids
Cissoid of Diocles
The classic cissoid is defined by:
y² = x³ / (2a − x)
A curve formed by tracing the intersection of a moving secant with a fixed circle.
y² = x³ / (2a − x)
A curve formed by tracing the intersection of a moving secant with a fixed circle.
The same curve in polar coordinates:
r = 2a / (1 + cosθ)
This form reveals its cusp structure and angular symmetry.
r = 2a / (1 + cosθ)
This form reveals its cusp structure and angular symmetry.
An equivalent variant sometimes used in optics:
r = a + b secθ
Shows how the curve explodes as the line approaches vertical.
r = a + b secθ
Shows how the curve explodes as the line approaches vertical.
Another beautiful identity:
x³ + y³ = 3axy
A cubic symmetric structure linking two mirrored branches.
x³ + y³ = 3axy
A cubic symmetric structure linking two mirrored branches.