Bristling Energy Page 3

Arms	Original	A (minibrot on straight)	B (minibrot on spiral)
2 in 4 out
	Period doubling. Size = 2.5E-27	Period doubling. Size = 3.1E-40	Period doubling. Size = 1.3E-57
4 in 8 out
	Period doubling. Size = 3.0E-31	Period doubling. Size = 3.8E-44	Period doubling. Size = 1.6E-61
8 in 4 out	No equivalent shape. The original fractal has 8 straight arms in this area.
		Period halving. Each even armed shape contains a minibrot. The center exit shape leaves with straight arms unlike the image to the right which has spiral arms. If you zoom into either 8 armed "candelabra" shape you would come to another shape like this one. Our path is down the center. Size = 5.0E-46	Period halving. Each even armed shape contains a minibrot. The center exit shape leaves with spiral arms. The arms interconnect differently than the one to the left. Size = 1.6E-63
4 in 8 out	No equivalent shape. The original fractal has 8 straight arms in this area.
		Period doubling. Similar to two rows above but 1E6 times smaller. Size = 1.4E-50	Period doubling. Similar to two rows above but 1E16 times smaller. Size = 7.0E-77
8 in 16 out
	Period doubling. The white dot at the center is the minibrot. Size = 3.5E-33	Period doubling. There is something interesting happening at the center. Size = 1.3E-52	Period doubling. There is something at the center here also. Size = 9.3E-79
16 in 8 out	No equivalent shape. This fractal has 16 straight arms in this area.
		Period halving. Leaves as straight arms. Size = 1.3E-53	Period halving. Leaves as a spiral. Size = 9.9E-80
8 in 16 out	No equivalent shape. This fractal has 16 straight arms in this area.
		Period doubling. Size = 1.0E-55	Period doubling. Size = 2.9E-86
16 in 32 out
	Period doubling. Zoomed to minibrot. The parameter file (bez34) for this image is located on page 4. Size = 4.4E-34	Period doubling. Size = 1.0E-56	Period doubling. Size = 3.6E-87
32 in 16 out
		Period halving. Leaves as straight arms. Size = 2.4E-57	Period halving. Leaves as spiral. Size = 9.0E-88
16 in 32 out
		Period doubling. Size = 2.5E-58	Period doubling. Size = 5.4E-91
32 in 64 out
		Period doubling. Size = 8.0E-59	Period doubling. Size = 1.8E-91
64 in 32 out
		Period halving. Size = 3.3E-59	Period halving. Size = 7.2E-92
32 in 64 out		No image for 32 in 64 out since it is visible as the light red area in the above image. Another simple period doubling.
			Period doubling. Size = 2.2E-93
64 in 128 out		No image for 64 in 128 out since it is visible as the dark red area in the above image. Another simple period doubling.
			Period doubling. Size = 1.1E-93
128 in 64 out
		Period halving. Zoomed to minibrot. The parameter file (beaz60) for this image is located on page 4. Size = 3.8E-60	Period halving. The minibrot can just start to be seen as the white dot in the center. Zooming deeper reveals the minibrot, but has features too fine to show up well in thumbnails of this size. The parameter file (bebz94) for this image is located on page 4. Size = 7E-94

In conclusion, the deeper minibrots have finer detail farther away from the center as you would expect. The original only has period doubling while A and B have period doubling and period halving. The period halving is associated with candelabra shapes that each contain a minibrot. It appears that any structure with an even number of arms always has a minibrot in it (except the two arm spiral). Zooming in on any minibrot away from the original seems to add period halving.

Zooming in on a minibrot on a spiral revealed a minibrot with spiral arms approaching it as well. Zooming in on a minibrot on a straight section had all straight arms.

I hope you enjoyed reading this short exploration into the mandelbrot set.

The next page has the FractInt parameter files for the deepest image in each column.