Precision Mathematical Drawing
Create stunning geometric art with hypotrochoid and epitrochoid equations. A parametric drawing tool for iOS.
Math meets ArtParametric Engine
Real-time curve generation with adjustable R, r, and d parameters. Every change renders instantly.
20+ Presets
Curated collection of geometric, natural, art, and traditional patterns to explore and customize.
Export Anywhere
Save as PNG at up to 4x resolution or scalable SVG. Share your creations without quality loss.
Dual Curve Modes
Switch between hypotrochoid and epitrochoid equations for fundamentally different geometries.
Live Preview
See your spirograph render in real-time as you adjust parameters. No waiting, no lag.
Mathematical Precision
GCD-based revolution calculation ensures every curve closes perfectly. No approximations.
Create Your Own
Pentagon Flower
5-petal flower with even spacing
Explore the Collection
Classic Star
R=96 r=36 d=36
Pentagon Flower
R=100 r=60 d=60
Triangle Loop
R=90 r=60 d=30
Hexagonal Web
R=84 r=72 d=48
Square Diamond
R=80 r=60 d=40
Rose Curve No.4
R=64 r=32 d=32
Daisy Pattern
R=100 r=75 d=75
Leaf Spiral
R=72 r=48 d=24
Sunflower
R=120 r=45 d=45
Seashell
R=100 r=33 d=50
Mandala Base
R=100 r=50 d=50
Infinity Loop
R=64 r=32 d=16
Stained Glass
R=150 r=50 d=75
Celtic Knot
R=90 r=30 d=60
Zen Circle
R=80 r=40 d=80
Classic Spirograph
R=64 r=32 d=16
Epicycloid Star
R=50 r=25 d=25
Cardioid
R=50 r=50 d=50
Nephroid
R=50 r=25 d=25
Astroid
R=80 r=20 d=20
The Equations
x(t) = (R - r) cos(t) + d · cos((R - r)/r · t)
y(t) = (R - r) sin(t) - d · sin((R - r)/r · t)
A curve traced by a point on a circle rolling inside a fixed circle.
x(t) = (R + r) cos(t) - d · cos((R + r)/r · t)
y(t) = (R + r) sin(t) - d · sin((R + r)/r · t)
A curve traced by a point on a circle rolling outside a fixed circle.
Rolling circle mechanism: the smaller circle rolls inside the larger, tracing the curve with a pen at offset d.