Chaos and fractals solutions

34. (a)

R S Theta Phi E F
.25 .25 0 0 0 0
.25 .25 0 0 .75 0
.25 .25 0 0 0 .75
.25 .25 0 0 .75 .75

R	S	E	F
.25	.25	0	0
.25	.25	.75	0
.25	.25	0	.75
.25	.25	.75	.75

(b)

R S Theta Phi E F
.1667 .1667 0 0 0 0
.1667 .1667 0 0 .833 0
.1667 .1667 0 0 0 .833
.1667 .1667 0 0 .833 .833

R	S	E	F
.1667	.1667	0	0
.1667	.1667	.833	0
.1667	.1667	0	.833
.1667	.1667	.833	.833

R	S	E	F
.4	.4	0	0
.4	.4	.6	0
.4	.4	0	.6
.4	.4	.6	.6

(e)

R S Theta Phi E F
(1-s)/2 (1-s)/2 0 0 0 0
(1-s)/2 (1-s)/2 0 0 (1+s)/2 0
(1-s)/2 (1-s)/2 0 0 0 (1+s)/2
(1-s)/2 (1-s)/2 0 0 (1+s)/2 (1+s)/2

R	S	E	F
(1-s)/2	(1-s)/2	0	0
(1-s)/2	(1-s)/2	(1+s)/2	0
(1-s)/2	(1-s)/2	0	(1+s)/2
(1-s)/2	(1-s)/2	(1+s)/2	(1+s)/2

(f) Take s = 0.5 in (e).

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