Fourier Epicycles — draw a logo with spinning circles

• 1 min read

Load an image, press Play, and two chains of spinning circles draw your logo. Fourier Epicycles is a Houdini SOP that turns the outline of a dark-on-light image into a Fourier series and animates every term as a circle.

How it works

The node traces the logo outline and computes its Fourier series. Each term becomes a circle spinning at its own frequency. The circles form two chains: the top chain sets the pen’s X position, the left chain sets its Y. The pen draws the logo where the two meet.

  • One Outline joins every piece of the logo, so a single pen draws it in one loop. Turn it off and every piece gets its own circles.
  • Auto-step adds circles each lap (1, 2, 3, 5 … 300), so you can watch the detail build up from a blob to the full shape.
  • Render-ready — every curve has width and Cd, so it renders in Karma as-is. Arms, circles, guides, ghost and trail sit in separate groups for separate looks.
  • Open asset — right-click → Allow Editing of Contents to read the VEX.

Source tab → Logo Image: pick a dark-on-light PNG or JPG. If parts are missing, change Trace Threshold. More Harmonics N = more circles per chain = more detail.

Requirements

Houdini 22, Indie or Apprentice (.hdalc). Includes the HDA, an example scene and a README.

Download

Get Fourier Epicycles

Installation

  1. Copy otls/sop_EMILSVFX.fourier_epicycles.1.0.hdalc to Documents/houdini22.0/otls/ (or Assets → Install Asset Library)
  2. In a Geometry node press Tab and type “Fourier Epicycles”
  3. Press Play

Questions or feature requests: emilsvfx@gmail.com