APPENDIX C
Sequence Unit Circle Variation Balls

• 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))

Unit Circle Example Ball

Sequence Unit Circle with Pseudocode

for (θ = 0; θ ≤ 36000; θ++)
{
	xnew = cos(0.01*θ);
	ynew = sin(0.01*θ);
   	PlotPoint(100.0*xnew, 100.0*ynew, color);
}

Example Ball with Pseudocode

for (θ = 0; θ ≤ 1800000; θ++)
{
	xnew = cos(0.4001*θ);
	ynew = sin(0.4001*θ);
	x = cos(θ);
	y = sin(θ);
	for (m = 0; m ≤ 19; m++)
	   PlotPoint(200.0*xnew+4.0*m*x, 200.0*ynew+4.0*m*y, color);
}

Ball	Build: (fa(θ),ga(θ))(fb(θ),gb(θ))	Scale: scalea, scaleb	Offset: mmin, mmax
Unit Circle	(cos(0.01*θ),sin(0.01*θ))(0.0, 0.0)	100.0, None	None, None
Example	(cos(0.4001*θ),sin(0.4001*θ))(cos(θ),sin(θ))	200.0, 4.0	0, 19
Ball #1	(cos(0.1101*θ)*sin(0.01*θ),sin(0.1101*θ)*sin(0.01*θ))(0.0, 0.0)	300.0, None	None, None
Ball #2	(cos(0.99*θ)*sin(0.02*θ),sin(0.99*θ)*sin(0.02*θ))(0.0, 0.0)	300.0, None	None, None
Ball #3	(cos(0.999*θ)*sin(0.0025*θ),sin(0.999*θ)*sin(0.0025*θ))(0.0, 0.0)	300.0, None	None, None
Ball #4	(cos(0.9*θ)*sin(0.9999*θ),sin(0.9*θ)*sin(0.9999*θ))(0.0, 0.0)	300.0, None	None, None
Ball #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))	200.0, 3.0	0, 51
Ball #6	(cos(0.5*θ)*sin(0.301*θ),sin(0.5*θ)*cos(0.301*θ))(cos(0.5*θ)*sin(0.301*θ),sin(0.5*θ)*cos(0.301*θ))	200.0, 3.0	0, 51
Ball #7	(cos(0.08*θ)*sin(0.998*θ),cos(0.999*θ))(cos(0.08*θ)*sin(0.998*θ),cos(0.999*θ))	200.0, 3.0	0, 51
Ball #8	(cos(θ),sin(θ))(cos(-0.301*θ)*sin(-0.501*θ)-sin(-0.501*θ)*sin(-0.301*θ),2.0*cos(-0.501*θ)*sin(-0.501*θ))	200.0, 3.0	0, 51
Ball #9	(cos(θ),sin(θ))(cos(-θ)*cos(-θ)-sin(-θ)*sin(-θ),2.0*cos(-θ)*sin(-θ))	200.0, 3.0	0, 51
Ball #10	(cos(θ),sin(θ))(cos(-1.01*θ),-sin(-1.01*θ))	200.0, 3.0	0, 51
Ball #11	(cos(θ),sin(θ))(cos(-0.5*θ),sin(-0.5*θ))	200.0, 3.0	0, 51
Ball #12	(cos(θ),sin(θ))(cos(-0.8001*θ),sin(-0.8001*θ)	200.0, 3.0	0, 51

Ball #1

Ball #2

Ball #3

Ball #4

Ball #5

Ball #6

Ball #7

Ball #8

Ball #9

Ball #10

Ball #11

Ball #12