## 3. Case Study of Aesthetic Forms

### 3-3 Recursive Multiple-level Relative Motions

One of the things computers are good at is performing dull repetitive tasks. In other words, a recursive procedure repeats itself. Recursive relative motion is a concept of peculiar motions. Figure 3-3 is shown as the difference between relative motions and recursive relative motions.

 Figure 3-3 Motions Illustration Rules: P0: P0(angle) = P0(angle) + P0(angular increment)       P0(x) = P2(x) + P0(radius) * P0(cos(angle))         P0(y) = P2(y) + P0(radius) * P0(sin(angle)) P1: P1(angle) = P1(angle) + P1(angular increment)       P1(x) = P0(x) + P1(radius) * P1(cos(angle))         P1(y) = P0(y) + P1(radius) * P1(sin(angle)) P2: P2(angle) = P2(angle) + P2(angular increment)       P2(x) = P1(x) + P2(radius) * P2(cos(angle))         P2(y) = P1(y) + P2(radius) * P2(sin(angle)) Trajectory Recorded: P0

Table: Case 3-3.1 Parameters Assigned (Figure 3-3.1)
 Point P1 P2 P0 Coordinate System P0 P1 P2 Initial Angle 0 0 0 Angular Increment -0.961003 0.2410107 -0.4810090 Radius(pixel) 1 1 1 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.1 (12,000,000 iterations)

Table: Case 3-3.2 Parameters Assigned (Figure 3-3.2)
 Point P1 P2 P0 Coordinate System P0 P1 P2 Initial Angle 0 0 0 Angular Increment -0.48003 0.24007 -0.35009 Radius(pixel) 1 1 1 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.2 (12,000,000 iterations)

Table: Case 3-3.3 Parameters Assigned (Figure 3-3.3)
 Point P1 P2 P0 Coordinate System P0 P1 P2 Initial Angle 0 0 0 Angular Increment -0.291252 0.388320 0.711920 Radius(pixel) 1 1 1 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.3 (2,500,000 iterations)

Table: Case 3-3.4 Parameters Assigned (Figure 3-3.4)
 Point P1 P2 P0 Coordinate System P0 P1 P2 Initial Angle 0 0 0 Angular Increment 0.2589 0.2912 -0.7766 Radius(pixel) 1 1 1 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.4 (7,500,000 iterations)

Table: Case 3-3.5 Parameters Assigned (Figure 3-3.5)
 Point P1 P2 P3 P0 Coordinate System P0 P1 P2 P3 Initial Angle 0 0 0 0 Angular Increment 0.30196 0.46667 -0.10980 -0.27493 Radius(pixel) 1 1 1 1 Radius Increment None None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.5 (24,000,000 iterations)

Table: Case 3-3.6 Parameters Assigned (Figure 3-3.6)
 Point P1 P2 P3 P0 Coordinate System P0 P1 P2 P3 Initial Angle 0 0 0 0 Angular Increment 0.25882 0.40000 -0.42353 -0.11801 Radius(pixel) 1 1 1 1 Radius Increment None None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.6 (24,000,000 iterations)

Table: Case 3-3.7 Parameters Assigned (Figure 3-3.7)
 Point P1 P2 P3 P4 P0 Coordinate System P0 P1 P2 P3 P4 Initial Angle 0 0 0 0 0 Angular Increment -2.2 0.3157286 -0.96 -0.12 -0.18 Radius(pixel) 1 1 1 1 1 Radius Increment None None None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.7 (12,000,000 iterations)

Table: Case 3-3.8 Parameters Assigned (Figure 3-3.8)
 Point P1 P2 P3 P4 P0 Coordinate System P0 P1 P2 P3 P4 Initial Angle 0 0 0 0 0 Angular Increment 0.08003 0.13 0.21 0.34 0.76 Radius(pixel) 1 1 1 1 1 Radius Increment None None None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.8 (1,800,000 iterations)

Table: Case 3-3.9 Parameters Assigned (Figure 3-3.9)
 Point P1 P2 P3 P4 P0 Coordinate System P0 P1 P2 P3 P4 Initial Angle 0 0 0 0 0 Angular Increment 0.12 0.19416 0.38832 0.72 -1.55328 Radius(pixel) 1 1 1 1 1 Radius Increment None None None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.9 (5,400,000 iterations)

Table: Case 3-3.10 Parameters Assigned (Figure 3-3.10)
 Point P1 P2 P3 P4 P0 Coordinate System P0 P1 P2 P3 P4 Initial Angle 0 0 0 0 0 Angular Increment 0.144000 0.232992 -0.698976 -1.164690 1.152000 Radius(pixel) 1 1 1 1 1 Radius Increment None None None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.10 (5,400,000 iterations)

Table: Case 3-3.11 Parameters Assigned (Figure 3-3.11)
 Point P1 P2 P3 P4 P5 P0 Coordinate System P0 P1 P2 P3 P4 P5 Initial Angle 0 0 0 0 0 0 Angular Increment 0.220066 0.066 -0.242 0.374 -0.506 -0.572 Radius(pixel) 1 1 1 1 1 1 Radius Increment None None None None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.11 (18,000,000 iterations)

Table: Case 3-3.12 Parameters Assigned (Figure 3-3.12)
 Point P1 P2 P3 P4 P5 P0 Coordinate System P0 P1 P2 P3 P4 P5 Initial Angle 0 0 0 0 0 0 Angular Increment 0.35 0.2900007 0.42 0.6400003 -2.10001 -1.30002 Radius(pixel) 1 1 1 1 1 1 Radius Increment None None None None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-3.12 (11,700,000 iterations)

CONTENTS:

 Index Introduction Methodology Case Study of Aesthetic Forms Conclusions