Complex-Valued Number Systems

lattice shape Hausdorff
dimension		 chir cov base base &
digits		 images
gaussian square 1 yes i·2
3
parallelogram 1pi 1 R yes −2
twindragon 1.523627 R no 1+i
yes −1−i
mandelbrot quintet 1.365212 L yes 2+i
mandelbrot nonet 1.7712437 L yes 3
island 4-13-2-0 L yes 3+i·2
island 4-13-1-2 L yes 3+i·2
archipelago 4-13-3-0 L yes 3+i·2
archipelago 4-13-1-3 L yes 3+i·2
archipelago 4-13-3-4 L yes 3+i·2
archipelago 4-13-5-1 L yes 3+i·2
archipelago 4-13-5-2 L yes 3+i·2
archipelago 4-13-3-5 L yes 3+i·2
1, i√2 rectangle r2 1 yes i√2
1, i√3 rectangle r3 1 yes i√3
eisenstein rhombus ir3d2 1 yes −2
gosper-lafitte triangle no 2
yes −1+i√3
crab fractal 1.5849625 yes −2
fudgeflake 1.261860 R no 3/2+i√3/2
yes −3/2+i√3/2
gosper island 1.129150 L yes 5/2+i√3/2
island 6-13-1-1,
tame 13-star		 1.254947 R yes 7/2+i√3/2
island 6-13-2-0,
wild 13-star		 1.5173088 R yes 7/2+i√3/2
island 6-13-1-2 R yes 7/2+i√3/2
archipelago 6-13-1-3 R yes 7/2+i√3/2
archipelago 6-13-2-3 R yes 7/2+i√3/2
feather 3 1.6575595 R no 3/2+i√3/2
3/2+i√3/2
yes −3/2−i√3/2
feather 7 R yes −5/2−i√3/2
kleinian tame twindragon 1.210761 L yes 1/2+i√7/2

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