SketchWave Clover Demo

Control Panel for SWClover Customization — Stage

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Control Panel

Clover Parameters

(Drag the center dot to reposition the figure)

Petals: 4

2 (nephroid) 3 (club ♣) 4 (clover ♧) 8

Radius (petal tip distance): 5.0

Small Large

Rotation (°): 0

0° 360°

Stroke Thickness: 2

Stroke Color & Opacity

Opacity: 100

Fill Color & Opacity

Opacity: 30

Center Dot

Show center dot

Center = (0.0, 0.0)

Opacity (Alpha): 100

Transparent — enables motion trails

Speed (°/sec, −720 to 720): 45

CW (−) CCW (+)

Oscillates the radius sinusoidally, making the clover gently expand and contract. The Radius display updates in real time. Try combining Breathe with Spin and a low Background opacity for glowing trails!

Speed (Hz): 0.5

Slow (0.1 Hz) Fast (2.0 Hz)

Amount (grid units): 1.5

Subtle Dramatic

Why "Clover"?

With numPetals = 4, the SWClover curve produces the classic four-leaf clover shape ☘ beloved as a symbol of good luck. With numPetals = 3, it creates the three-lobed club symbol ♣ of a playing card suit. Higher petal counts produce elegant multi-petaled rosettes. All these shapes are epicycloids — curves traced by a point on a small circle rolling around the outside of a fixed circle.

The Parametric Equations

SWClover uses epicycloid parametric equations. For API parameter numPetals, the internal epicycloid parameter n is set to numPetals + 1, and scale factor a = radius / numPetals ensures each petal tip lands exactly radius units from the center:

n = numPetals + 1
a = radius / numPetals

x(t) = a · (n · cos(t) − cos(n · t))
y(t) = a · (n · sin(t) − sin(n · t))

t ∈ [0, 2π)

Special Values of numPetals

numPetals	n (internal)	Shape
2	3	Nephroid — 2-cusped kidney shape
3	4	3-petal epicycloid — club ♣ shape
4	5	4-leaf clover ☘ (default)
5	6	5-petal rosette
6	7	6-petal flower
7–8	8–9	Dense multi-petal rosette

Epicycloids in Mathematics

An epicycloid is traced by a point on the rim of a small circle of radius a rolling around the outside of a fixed circle of radius R. The ratio R/a determines the number of cusps:

R/a = 1 (n = 2): cardioid (1 cusp)
R/a = 2 (n = 3): nephroid (2 cusps)
R/a = 3 (n = 4): 3-cusp epicycloid ♣
R/a = 4 (n = 5): 4-cusp epicycloid ☘

Famous epicycloid curves appear in gear design (hypocycloidal gears), the Spirograph toy, and the mathematics of complex analysis. The nephroid was first described by Huygens (1678); the term "epicycloid" was introduced by Ole Rømer around 1674 while designing gears.

The Breathe Animation

SWClover's signature animation is Breathe, which oscillates the petal radius sinusoidally — the clover gently expands and contracts like a breathing organism. The Radius display updates in real time. Combine Breathe with Spin and low Background opacity for glowing ghosted trails!

Using the Controls

Petals — number of clover lobes. 3 = club; 4 = clover; higher = rosette.
Radius — distance from center to each petal tip in grid units.
Rotation — rotates the figure. Useful for aligning petals on diagonals.
Breathe (accordion) — sinusoidally oscillates the radius. Speed sets Hz; Amount sets the radius swing in grid units.
Spin (accordion) — continuously rotates the clover. Combine with Breathe for complex patterns.
Drag the center dot to reposition the figure.
Click the canvas to toggle the grid on/off.

Keyboard Shortcuts

s — Toggle spin
b — Toggle breathe
r — Factory reset
q — Stop all animations

SketchWave Clover Demo

Control Panel

Clover Parameters

Background

Spin (Rotation)

Breathe (Radius Oscillation)