APPENDIX G
Dimension Variations

• x_a = f_a(θ)
• y_a = g_a(θ)
• x_b = f_b(θ)
• y_b = g_b(θ)
• m_min ≤ m ≤ m_max
• scale = scale_a,scale_b
• point = ((scale_a*x_a + scale_b*x_b*m),(scale_a*y_a + scale_b*y_b*m))

Dimension Example with Pseudocode

Dimension Example

for (int θ = 0; θ ≤ 500000; θ++)
{
	xnew = cos( 0.4001*θ);
	ynew = sin(-0.4001*θ);
	x = cos(θ);
	y = sin(θ);
	for (int m = 1; m ≤ 20; m++)
        PlotPoint(xnew*300.0+m*x*4.0, ynew*300.0+m*y*4.0, color);
}

Dimension	Build: (fa(θ),ga(θ))(fb(θ),gb(θ))	Scale: scalea,scaleb	Offset: mmin,mmax
Example	(cos(0.4001*θ),sin(-0.4001*θ))((cos(θ),sin(θ))	300.0,4.0	1,20
Dimension #1	(cos(0.4*θ),sin(0.9001*θ))(cos(0.4*θ)*sin(θ),0.3*sin(θ))	375.0,4.0	0,19
Dimension #2	(cos(0.4001*θ),sin(0.42001*θ))(cos(θ),sin(θ))	300.0,4.0	1,19
Dimension #3	(cos(0.4001*θ),sin(-0.4008*θ))(cos(θ),sin(θ))	300.0,4.0	0,19
Dimension #4	(cos(θ),sin(θ))(cos(0.001*θ),sin(0.001*θ))	200.0,3.0	0,51
Dimension #5	(cos(0.301*θ)*sin(0.302*θ),sin(0.301*θ))(cos(0.301*θ)*sin(0.302*θ),sin(0.301*θ))	225.0,3.0	0,51
Dimension #6	(cos(0.500*θ)*sin(0.301*θ),sin(0.500*θ)*cos(0.301*θ))(cos(0.500*θ)*sin(0.301*θ),sin(0.500*θ)*cos(0.301*θ))	225.0,3.0	0,51
Dimension #7	(cos(0.081*θ)*tan(0.081*θ),cos(0.081*θ)*cos(0.080*θ))(cos(0.081*θ)*tan(0.081*θ),cos(0.081*θ)*cos(0.080*θ))	225.0,3.0	0, 51
Dimension #8	(cos(0.0311*θ)*tan(0.0311*θ)),cos(0.001*θ)*tan(0.001*θ))(cos(0.0311*θ)*tan(0.0311*θ)),cos(0.001*θ)*tan(0.001*θ))	225.0,3.0	0, 51
Dimension #9	(cos(-0.7503*θ), sin(0.501*θ)) (cos(θ), sin(θ))	200.0, 3.0	0, 51
Dimension #10	(cos(θ), sin(θ)) (cos(0.99*θ)*tan(0.99*θ)-sin(0.99*θ)*sin(0.99*θ), 2.0*cos(0.99*θ)*sin(0.99*θ))	200.0, 3.0	0, 51
Dimension #11	(cos(θ), sin(θ)) (cos(0.01*θ)*cos(0.01*θ)-sin(-0.994*θ)*sin(-0.994*θ), 2.0*cos(0.01*θ)*sin(-0.994*θ))	200.0, 3.0	0, 51
Dimension #12	(cos(0.0023*θ), sin(0.0043*θ)) (cos(θ), sin(θ))	300.0, 4.0	0, 19

Dimension #1

Dimension #2

Dimension #3

Dimension #4

Dimension #5

Dimension #6

Dimension #7

Dimension #8

Dimension #9

Dimension #10

Dimension #11

Dimension #12