On Fractals and Ancient Art Work Part 2

Tags

Ancient Art Work, Chaos Game, fractals, tools

Fractals and Ancient Art Work Part 2. The fractals below resemble ancient art work and were generated with the Chaos Game Explorer tool by playing the game 100,000 times using a polygon with n vertices and a scaling ratio r.

Showing below are:

(a) a calendar-like pattern with faces watching you (n = 13, r = 0.30)

(b) a mandala-like pattern (n = 20, r = 0.30)

(c) a collar-like (or plate-like) pattern (n = 40, r = 0.20).

Pixels were color coded in white. Multi-coloring the pixels reveals these simply are the result of partially overlapping a given pattern across many scales.

Again: Did ancient cultures know about this way of generating art work? Feel free to try the tool with other parameter values, compare results by searching in Google Images for the resembled image, and share results.

Let me know if you find something interesting. I’m documenting results.

This is the second part of a previous post.

On Fractals and Ancient Art Work

Tags

Ancient Art Work, Barnsley Algorithm, Chaos, Chaos Game Explorer, Fractal Patterns, fractals

The figure was generated with our Chaos Game Explorer tool, using the algorithm described at

http://www.minerazzi.com/tools/chaos-game/chaos-game.php

and as presented in Barnsley’s books (Fractals Everywhere, 1988; The Desktop Fractal Design HandBook, 1989).

The game was played N = 100,000 times by randomly placing a point within an n-gon (polygon with n vertices), using different combinations of vertices (n) and scale ratios (r), and by coloring in white the emerging patterns. Some combinations produce patterns somehow resembling ancient calendars, medallions, rings,… from different ancient cultures.

For the above figure, I used n = 12 and r = 0.30.

Running the algorithm by coding the pixels in different colors reveals that the patterns are just the result of partially overlapping the same n-gon across many scales of observations. Did ancient cultures know about this technique?

Just for fun, you may want to try with other values, then run searches in Google Images for ancient calendars, medallions, rings, etc and compare results. Share your images and let me know if you found something interesting. I’m documenting results.