Fourier Epicycle Drawing Studio

✏️ Draw anything on the canvas with your mouse/touch, or select a preset!

⚡ Streamlit Cloud Studio

Run the full Python studio online: 4096-harmonic precision, background music looping, and instant MP4 video downloads.

Shape Source

Select Curve / Contour

Epicycle Architecture

Fourier Parameters

Harmonics (N): 100

Simulation Speed: 1.0x

Show Epicycle Circles

Show Perpendicular Guides

Pen Tip Glow & Trace

Harmonic Metrics

Active Harmonics

100

Curve Fit

99.98%

Angle (t)

0.00 rad

Sample Points

1024

Mathematical Formula

x_N(t) = a₀/2 + \sum [a_k\cdotcos(kt) + b_k\cdotsin(kt)] y_N(t) = c₀/2 + \sum [c_k\cdotcos(kt) + d_k\cdotsin(kt)] Guides extend from X(t) and Y(t) tips to meet at pen [x_N(t), y_N(t)].