10182

Generalized Straightedge and Compass Fractal

Define "the circles of a triangle" to mean the three circles centered at the vertices of the triangle with a radius equal to the "length multiplier" times the edge length of the triangle (it is most natural to let the length multiplier equal 1).
Given a triangle , the vertices of its midpoint triangle are the midpoints of the sides of . A fractal is made by starting with an equilateral triangle and at each iteration adding vertices of any midpoint triangle and circles at these vertices, as well as at any vertex generated at a prior iteration, with the radius of the circles added at an iteration equal to the product of the length multiplier and the edge length of the midpoint triangles added at that iteration.
Alternatively, apply the replacement rules shown in white at the top wherever possible.

DETAILS

An exploration of the dynamics of this system is given in my YouTube video [1], where I describe how to make this fractal using only straightedge and compass.
Reference
[1] R. Southwell. The Generalized Circle Fractal: Exploration & Straightedge-Compass Construction [Video]. (Jun 2, 2014) www.youtube.com/watch?v=pX09sJSdr9I.

PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.