![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8JQNCC23Ofp6S1W2INN-oSJi3PMbNkIn37dCg1jYa4pKDCtPo8UGBYSy93ymf98QNKnGBEE38Y7z43MCYXUP0XN1COs_auRd396lWhKNhTorqVu4cidM6A2uOsVwUnYgRLM5Q/s320/fractal.png)
I have implemented a fractal in HTML5 canvas: http://www.byronknoll.com/kites.html. It is based on a fractal discovered by Robert Fathauer. Here is a zoomed-in view of the top of my fractal:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinZSeJ09j6ta2gJNLuW0anHL7ewsyX_xTVIW0Dxdk-jt87tLV2f5d36KbAOScKnFKxgqVp9oNWHBWon-NTnPq5AvZuzofTuapXV8XUSNd4KITLa-7uZeLvOmgEhqRl3yQejMgh/s320/zoomed.png)
The fractal seems to have some interesting properties. Near the center of the zoomed-in image above you can see a "tunnel" of consecutively smaller triangles. There are an infinite number of these tunnels (and I think they exist in every direction). Along the vertical you can see there is pattern to the location of the tunnels. The distance between the tunnels is a geometric sequence with a common ratio of 1/3. As you travel into a tunnel, the hypotenuse length of consecutive triangles is also a geometric sequence with the same common ratio of 1/3.
No comments:
Post a Comment