The following images are the product of Rotational Fractal, which I happened to discover a few years ago. I am not sure whether mathematicians are using any similar method to generate fractals.
I found this method quite versatile in creating many unusual fractals.
The example below has been generated using Dodecagon as a seed. In order to generate this I have used mirroring and arraying extensively to achieve each empty areas confined by dodecagons, which is represented by blue patterns below. Each pattern, starting with triangle, represents different level of mirroring and arraying. Please refer to my Rotational Fractal page for more details.
The second image has been scaled down due to its enormity. Otherwise, it wouldn't fit here if in scale.
I have noticed that fractals created this way can generate different image depending on the location of axis of mirroring.
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The following illustrations show how they are achieved.
The blue triangles are formed sorrounded by 6 dodecagons.
the six dodecagons above are mirrored and arrayed around the centre. you can observe that a new and bigger areas appear.
The process is repeated several times to get other configurations in the first 2 configurations. Note that the resulting configurations depend on where you apply the mirroring axis.
The illustration below shows all varying empty areas confined by surrounding dodecagons.
The following image show two different fractals produced by varing the position of mirroring axes. This may explain the fact that there are so many different type of snowflakes in nature. A minor difference in early part of arraying and mirroring may signicantly change overall shape within the confinement of hexagonal configuration.
Apart from any mathematical consideration, how marvelous these patterns are!
Wouldn't you like to frame it and hang it in your lounge?
