Rotational Fractals

While I was experimenting with Rotational Pattern Technique, I happened to observe an interesting phenomenon that lead to some interesting fractals. I am not a mathematician, so I cannot fathom its implication. But I suspect there might be some sort of underlying relationship that might be of some importance.

It is possible to create fractals with various polygons, but for the purpose of showing what this technique is capable of, hexagon is selected.

1. Mirror the hexagon around an axis that coincides with any of its 6 sides.

2. Array the mirrored hexagon 6 times around the center of the first one as shown below.

3. Consider the above 7 hexagons as a unit and again mirror this unit around an axis.

4. As in 2, array the mirrored unit 6 times around the center of the first one.

As you can see the fractal outline is taking shape.

5. Consider the above cluster of hexagons as a unit and repeat the procedure as in 3.

6. Array the mirrored cluster 6 times around the center of the first one.

Notice the emergence of the new type of fractal as shown in the purple turtles.

7. Continue with the above procedures until the desired degree of complexity is achieved.

This image is produced only after 4th iteration using hexagon as a seed. Now, upon close inspection of the pattern, 2 hexagonal fractals emerge. The first one can be found by tracing the outline surrounded by navy blue, which is shown below.

The second one is the negative of the above image as shown below.

Compare these with the Koch Snowflake. While Kosh Snowflake is based on triangle( triangular fractals), these are built with hexagons. Also notice the difference between these two hexagonal fractals which were produced simultaneously employing rotational pattern technique.

Also note that most of the fractals on this website have been created employing this technique. Check Fractals pages for more examples.