0.3
0.7

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Spirograph is a pattern made by tracing a point on a smaller circle spinning inside a larger circle. Radius ratio specifies the relative sizes of the two circles. Pen position is the radial position of the point inside the inner circle that is being traced. More on Wikipedia and Wolfram Mathworld.

Pendulum
1
2
3

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A three-pendulum Harmonograph is a device that uses two pendulums to move a pen and a third pendulum to move a drawing surface. Each pendulum has an amplitude in X and Y direction, a frequency and a damping coefficient associated with it. Because of the combined complexity of this system, then pen traces fascinating patterns on the drawing surface. More on Wikipedia.

Component
X
Y

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Trig1 pattern uses a parametric curve defined using a polynomial of simple trigonometric functions - sine and cosine. The function form involving two sets of amplitudes (A) and frequencies (F) for x and y as well as two exponents i and j is shown below.

Equations used to plot trig1 pattern.
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A simple idea: Create interesting patterns using a few parameteric curves and colors. Scroll down to see some examples or use the webapp to generate your own patterns.

Splash image showing a curve generated using 2 pendulum harmonograph