Home Page.
Related Page.

Pinwheel pattern for the reverse operation.

For this example, 288 (= 17 × 17 − 1) complex lichts of breadth of 9 were created.

All have the same divisors, which came from a random number generator:

A𝗗 = (	[−2.157831, +2.036379],	[−1.613613, −0.530356],	[+1.266265, +0.314028],
	[+1.609747, +0.060905],	[+2.574440, +2.426379],	[−0.384536, +0.795593],
	[+2.399972, +1.861534],	[−1.071064, −0.443848],	[+0.077443, +1.506880]	)

There are 288 different values for A_𝗟0. Each of them has for the real part an integer x in the range −8 ≤ x ≤ +8; and similarly for the imaginary part y. Omitted is [0, 0] because it leads to a panagon.

Here for instance are all the lengths for the case where A_𝗟0 = [−8, −8], which is in the upper-left corner of the table:

A𝗟 = (	[−8.000000, −8.000000],	[−1.337221, +6.639450],	[+0.769654, −7.040293],
	[+0.900147, −9.599829],	[+2.972378, −10.20704],	[−1.293254, −5.178448],
	[−9.578399, +4.832536],	[−3.903366, +4.911590],	[+4.661360, −8.405169]	)

For each of the 288 values of A, the table below lists (rev (A))_𝗚, using the character P to symbolize a panagon. Evident is that the gons form a pinwheel pattern. Remaining to be investigated is whether the boundaries between gon zones exhibit fractal behavior.

		y =
		−8	−7	−6	−5	−4	−3	−2	−1	0	+1	+2	+3	+4	+5	+6	+7	+8
x =	−8	6	6	6	6	6	5	5	5	5	5	5	4	4	4	4	4	4
	−7	6	6	6	6	6	6	5	5	5	5	5	4	4	4	4	4	4
	−6	6	6	6	6	6	6	5	5	5	5	4	4	4	4	4	4	4
	−5	6	6	6	6	6	6	5	5	5	5	4	4	4	4	4	4	3
	−4	7	6	6	6	6	6	6	5	5	5	4	4	4	4	4	3	3
	−3	7	7	7	6	6	6	6	5	5	4	4	4	4	3	3	3	3
	−2	7	7	7	7	7	6	6	6	5	4	4	4	3	3	3	3	3
	−1	7	7	7	7	7	7	7	6	5	4	3	3	3	3	3	3	3
	0	7	7	7	7	7	7	7	7	P	3	3	3	3	3	3	3	3
	+1	7	7	7	7	8	8	8	8	0	2	2	2	2	2	2	2	3
	+2	8	8	8	8	8	8	8	0	0	1	2	2	2	2	2	2	2
	+3	8	8	8	8	8	8	0	0	0	1	1	2	2	2	2	2	2
	+4	8	8	8	8	8	0	0	0	0	1	1	1	2	2	2	2	2
	+5	8	8	8	8	8	0	0	0	0	1	1	1	1	2	2	2	2
	+6	8	8	8	8	0	0	0	0	0	1	1	1	1	1	2	2	2
	+7	8	8	8	0	0	0	0	0	0	1	1	1	1	1	1	2	2
	+8	8	8	0	0	0	0	0	0	0	1	1	1	1	1	1	1	2