Curve Catalog

Browse the built-in curves. Each curve has unique geometry, period, and behavior. Click any curve to see the details of its equation, parameters, and a live preview.

Available Curves

Standard

Some of the well-known and well-documented curves with easy to find mathematical definitions.

Their commonality does not take away from their inherent beauty

Rose (n=3)

A 3-petaled rose curve with trifold symmetry. Also used as the Sarmal logo.

Rose (n=5)

A 5-petaled rose curve with fivefold symmetry.

Rose (n=5/2)

A 5-petaled rose with a fractional exponent that requires two full revolutions to close, producing elegant trail crossings through the center.

Epitrochoid

A roulette tracing 7 lobes with an animated distance parameter that creates organic motion.

Astroid

A hypocycloid with 4 sharp cusps, forming a star-like shape within a square.

Deltoid

A 3-cusped hypocycloid tracing a triangle-like curve.

Lissajous 3:2

A figure-eight-like curve with a slowly drifting phase that causes the skeleton to morph continuously.

Lissajous 4:3

A more complex Lissajous pattern with 4:3 frequency ratio and drifting phase.

Epicycloid (n=3)

A 3-pointed star shape created by a point on a rolling circle.

Lamé Curve

A superellipse that morphs continuously between diamond, circle, and squircle shapes.

Star

A 5-pointed star built from Fourier harmonics in polar coordinates.

Star (4-arm)

A 4-pointed star using the same Fourier harmonic construction as Star.

Star (7-arm)

A 7-pointed star using the same Fourier harmonic construction as Star.

Iconic

These are mainly tributes to the impactful happenings of nature, humanity and univcerse. A recreation of shapes from the real world, whose silhouttes carry a deeper meaning beyond their mathematical equations.

Artemis II

Modified lemniscate with two unequal lobes.

Quick Reference