Explore the fractal online at
http://demonstrations.wolfram.com/GeneralizedStraightedgeAndCompassFractal/
I recently found this interesting fractal which could be created from a triangle in a very simple way.
The basic idea is to start with an equilateral triangle, and keep the new finding midpoint triangles, and then
adding the `circles' of those triangles. Here, by `the circles of a triangle' I mean the three circles centered around the vertices of the triangle, which have a radius equal to m times the edge-length of the triangle (where m=1).
By repeatedly creating the new midpoint triangles, and their circles I created the interesting patterns described in my previous videos (see below for links).
However, today I started to look at what happens when one changes the circle-radius multiplier m. If one creates a configuration of circles by running the original system for a given number of iterations, and then one alters the value of the
`multiplier' m one sees the circles change size and position in a beautiful way.
In this video I give a rough outline of the idea behind the systems, then I show how the configurations of circles change as the multiplier is changed from 0 to 3, then I describe how these patterns can be made via a straightedge and compass construction (using GeoGebra).
New Compass And Straightedge Fractal Explored In Color
https://www.youtube.com/watch?v=QNuZ9yXdev0
A New Fractal Created With Compass And Straight Edge
https://www.youtube.com/watch?v=SGDQkncxia0
http://www.geogebra.org/cms/en/
https://sites.google.com/site/richardsouthwell254/home