## 3. Case Study of Aesthetic Forms

### 3-4 Pursuit Multiple-level Relative Motions

#### 3-4-1 Case I: Pursue the farthest coordinate system

 Figure 3-4a Motions Illustration Initial State: P4 pursues P1, velocity = 1 (pixels per iteration) Rules: P0: P0(x, y) = (0, 0) P1: P1(angle) = P1(angle) + P1(angular increment)      P1(x) = P3(x) + P1(radius) * P1(cos(angle))      P1(y) = P3(y) + P1(radius) * P1(sin(angle)) P2: P2(angle) = P2(angle) + P2(angular increment)      P2(x) = P3(x) + P2(radius) * P2(cos(angle))      P2(y) = P3(y) + P2(radius) * P2(sin(angle)) P3: P3(angle) = P3(angle) + P3(angular increment)      P3(x) = P0(x) + P3(radius) * P3(cos(angle))      P3(y) = P0(y) + P3(radius) * P3(sin(angle))

We set the rules of P4 as follow below:

P4: d1 = distance(P1, P4)
d2 = distance(P2, P4)
d3 = distance(P3, P4)
if d1 equals the greatest of d1, d2 and d3, then
let P4 pursue P1
end if
if d2 equals the greatest of d1, d2 and d3, then
let P4 pursue P2
end if

if d3 equals the greatest of d1, d2 and d3, then
let P4 pursue P3
end if
Trajectory Recorded: P4

Table: Case 3-4.1 Parameters Assigned (Figure 3-4.1)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 0 180 0 Angular Increment 0.05 -0.15 0.06404658 Radius(pixel) 300 220 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.1 (18,000,000 iterations)

Table: Case 3-4.2 Parameters Assigned (Figure 3-4.2)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 0 180 0 Angular Increment 0.05 -0.15 0.06405 Radius(pixel) 300 120 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.2 (18,000,000 iterations)

Table: Case 3-4.3 Parameters Assigned (Figure 3-4.3)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 0 180 0 Angular Increment 0.03 -0.27 0.06405 Radius(pixel) 300 120 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.3 (18,000,000 iterations)

Table: Case 3-4.4 Parameters Assigned (Figure 3-4.4)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 0 180 0 Angular Increment 0.03 -0.27 0.06405 Radius(pixel) 300 220 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.4 (18,000,000 iterations)

Table: Case 3-4.5 Parameters Assigned (Figure 3-4.5)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 180 0 0 Angular Increment -0.03 0.27 0.06405 Radius(pixel) 300 150 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.5 (18,000,000 iterations)

Table: Case 3-4.6 Parameters Assigned (Figure 3-4.6)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 0 180 0 Angular Increment 0.05 -0.15 0.154047 Radius(pixel) 300 120 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.6 (18,000,000 iterations)

Table: Case 3-4.7 Parameters Assigned (Figure 3-4.7)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 0 180 0 Angular Increment 0.07 -0.14 0.284047 Radius(pixel) 300 120 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.7 (18,000,000 iterations)

#### 3-4-2 Case I: Pursue the nearest coordinate system

We modify the rules of P4 as follow below:

P4: d1 = distance(P1, P4)
d2 = distance(P2, P4)
d3 = distance(P3, P4)
if d1 equals the smallest of d1, d2 and d3, then
let P4 pursue P1
end if
if d2 equals the
smallest of d1, d2 and d3, then
let P4 pursue P2
end if
if d3 equals the
smallest of d1, d2 and d3, then
let P4 pursue P3
end if
Trajectory Recorded: P4

Table: Case 3-4.8 Parameters Assigned (Figure 3-4.8)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 0 0 0 Angular Increment -0.47000000 0.51000000 0.48404658 Radius(pixel) 170 120 200 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.8 (18,000,000 iterations)

Table: Case 3-4.9 Parameters Assigned (Figure 3-4.9)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 0 180 0 Angular Increment 0.420100 -0.640300 0.384047 Radius(pixel) 200 130 200 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.9 (12,000,000 iterations)

Table: Case 3-4.10 Parameters Assigned (Figure 3-4.10)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 180 0 0 Angular Increment 0.140000 -0.260010 0.284047 Radius(pixel) 100 150 180 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.10 (18,000,000 iterations)

Table: Case 3-4.11 Parameters Assigned (Figure 3-4.11)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 0 180 0 Angular Increment 0.240000 -0.080000 0.284047 Radius(pixel) 300 120 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.11 (18,000,000 iterations)

Table: Case 3-4.12 Parameters Assigned (Figure 3-4.12)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 0 180 0 Angular Increment -0.180000 -0.030010 0.684047 Radius(pixel) 300 120 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.12 (18,000,000 iterations)

Table: Case 3-4.13 Parameters Assigned (Figure 3-4.13)
 Point P1 P2 P3 Coordinate System P3 P3 P0 Initial Angle 180 0 0 Angular Increment 0.160000 -0.250010 0.684047 Radius(pixel) 300 220 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.13 (18,000,000 iterations)

#### 3-4-3 Case II: Pursue the farthest coordinate system

 Figure 3-4b Motions Illustration Initial State: P4 pursues P1, velocity = 1 (pixels per iteration) Rules: P0: P0(x, y) = (0, 0) P1: P1(angle) = P1(angle) + P1(angular increment)      P1(x) = P2(x) + P1(radius) * P1(cos(angle))      P1(y) = P2(y) + P1(radius) * P1(sin(angle)) P2: P2(angle) = P2(angle) + P2(angular increment)      P2(x) = P3(x) + P2(radius) * P2(cos(angle))      P2(y) = P3(y) + P2(radius) * P2(sin(angle)) P3: P3(angle) = P3(angle) + P3(angular increment)      P3(x) = P0(x) + P3(radius) * P3(cos(angle))      P3(y) = P0(y) + P3(radius) * P3(sin(angle))

We set the rules of P4 as follow below:

P4: d1 = distance(P1, P4)
d2 = distance(P2, P4)
d3 = distance(P3, P4)
if d1 equals the greatest of d1, d2 and d3, then
let P4 pursue P1
end if
if d2 equals the greatest of d1, d2 and d3, then
let P4 pursue P2
end if

if d3 equals the greatest of d1, d2 and d3, then
let P4 pursue P3
end if
Trajectory Recorded: P4

Table: Case 3-4.14 Parameters Assigned (Figure 3-4.14)
 Point P1 P2 P3 Coordinate System P2 P3 P0 Initial Angle 0 0 0 Angular Increment 0.035330 -0.547783 -0.047300 Radius(pixel) 150 100 150 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.14 (12,000,000 iterations)

Table: Case 3-4.15 Parameters Assigned (Figure 3-4.15)
 Point P1 P2 P3 Coordinate System P2 P3 P0 Initial Angle 0 0 0 Angular Increment -0.047300 -0.547783 0.035330 Radius(pixel) 150 100 150 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.15 (12,000,000 iterations)

Table: Case 3-4.16 Parameters Assigned (Figure 3-4.16)
 Point P1 P2 P3 Coordinate System P2 P3 P0 Initial Angle 0 0 0 Angular Increment 0.047300 -0.035330 0.547783 Radius(pixel) 150 150 100 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.16 (12,000,000 iterations)

#### 3-4-4 Case II: Pursue the nearest coordinate system

We modify the rules of P4 as follow below:

P4: d1 = distance(P1, P4)
d2 = distance(P2, P4)
d3 = distance(P3, P4)
if d1 equals the smallest of d1, d2 and d3, then
let P4 pursue P1
end if
if d2 equals the
smallest of d1, d2 and d3, then
let P4 pursue P2
end if
if d3 equals the
smallest of d1, d2 and d3, then
let P4 pursue P3
end if
Trajectory Recorded: P4

Table: Case 3-4.17 Parameters Assigned (Figure 3-4.17)
 Point P1 P2 P3 Coordinate System P2 P3 P0 Initial Angle 0 0 0 Angular Increment -0.5967700 0.3090170 -0.4075677 Radius(pixel) 70 100 180 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.17 (12,000,000 iterations)

Table: Case 3-4.18 Parameters Assigned (Figure 3-4.18)
 Point P1 P2 P3 Coordinate System P2 P3 P0 Initial Angle 0 0 0 Angular Increment 0.5967700 0.3090170 0.4075677 Radius(pixel) 70 100 180 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.18 (12,000,000 iterations)

Table: Case 3-4.19 Parameters Assigned (Figure 3-4.19)
 Point P1 P2 P3 Coordinate System P2 P3 P0 Initial Angle 0 0 0 Angular Increment 0.8967700 -0.3090170 0.5075677 Radius(pixel) 70 100 180 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.19 (12,000,000 iterations)

Table: Case 3-4.20 Parameters Assigned (Figure 3-4.20)
 Point P1 P2 P3 Coordinate System P2 P3 P0 Initial Angle 0 0 0 Angular Increment 0.6967700 -0.3090170 0.5075677 Radius(pixel) 170 100 180 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.20 (12,000,000 iterations)

Table: Case 3-4.21 Parameters Assigned (Figure 3-4.21)
 Point P1 P2 P3 Coordinate System P2 P3 P0 Initial Angle 0 0 0 Angular Increment 0.6967700 -0.3090170 0.5075677 Radius(pixel) 170 150 180 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.21 (12,000,000 iterations)

Table: Case 3-4.22 Parameters Assigned (Figure 3-4.22)
 Point P1 P2 P3 Coordinate System P2 P3 P0 Initial Angle 0 0 0 Angular Increment 0.3967700 -0.3390170 0.5075677 Radius(pixel) 170 50 180 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
Figure 3-4.22 (12,000,000 iterations)

CONTENTS:

 Index Introduction Methodology Case Study of Aesthetic Forms Conclusions