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3. Case Study of Aesthetic Forms

3-5 Chaotic Pursuit Multiple-level Relative Motions


Figure 3-5 Motions Illustration

Initial State:
P5 pursues P1, velocity = 1 (pixels per iteration)

Rules:
P0: P0(x, y) = (400, 300)

P1: P1(angle) = P1(angle) + P1(angular increment)

     P1(x) = P4(x) + P1(radius) * P1(cos(angle))

     P1(y) = P4(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: if P3(radius) < 0 or P3(max radius) > 120, then

         set P3(radius increment) to P3(radius increment) * (-1)

     end if

     P3(radius) = P3(radius) + P3(radius increment)

     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))

P4: P4(angle) = P4(angle) + P4(angular increment)

     P4(x) = P3(x) + P4(radius) * P4(cos(angle))

     P4(y) = P3(y) + P4(radius) * P4(sin(angle))

P5: d1 = distance(P1, P5)

     d2 = distance(P2, P5)

     if d1 is less than or equal to 8 and d2 is less than or equal to 8, then

          if P5 is pursuing P1, then

               let P5 pursue P2

          else if P5 is pursuing P2, then

               let P5 pursue P1

          end if

     end if


Chaotic Terms:
     if P5(y) is greater than P3(y), then

          set P1(angular increment) to P1(angular increment) * (-1)

     end if
Trajectory Recorded: P5


Table: Case 3-5.1 Parameters Assigned (Figure 3-5.1)
Point
P1
P2
P3
P4
Coordinate System
P4
P3
P0
P3
Initial Angle
0
180
0
0
Angular Increment
0.2401201
-0.1801864
0.15
-0.21
Radius(pixel)
30
160
120
120
Radius Increment
None
None
-0.1
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-5.1 (9,000,000 iterations)

Table: Case 3-5.2 Parameters Assigned (Figure 3-5.2)
Point
P1
P2
P3
P4
Coordinate System
P4
P3
P0
P3
Initial Angle
0
180
0
0
Angular Increment
0.1801201
-0.1501864
0.1200000
-0.0900000
Radius(pixel)
30
160
120
120
Radius Increment
None
None
-0.1
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-5.2 (12,000,000 iterations)

Table: Case 3-5.3 Parameters Assigned (Figure 3-5.3)
Point
P1
P2
P3
P4
Coordinate System
P4
P3
P0
P3
Initial Angle
0
180
0
0
Angular Increment
0.2701201
-0.2101864
0.1800000
-0.1500000
Radius(pixel)
30
160
120
120
Radius Increment
None
None
-0.1
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-5.3 (12,000,000 iterations)

Table: Case 3-5.4 Parameters Assigned (Figure 3-5.4)
Point
P1
P2
P3
P4
Coordinate System
P4
P3
P0
P3
Initial Angle
0
180
0
0
Angular Increment
0.2401201
-0.1801864
-0.1200000
0.1500000
Radius(pixel)
30
160
120
120
Radius Increment
None
None
-0.1
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-5.4 (12,000,000 iterations)

Table: Case 3-5.5 Parameters Assigned (Figure 3-5.5)
Point
P1
P2
P3
P4
Coordinate System
P4
P3
P0
P3
Initial Angle
0
180
0
0
Angular Increment
-0.1201201
0.1801864
0.1700000
-0.1300000
Radius(pixel)
20
160
120
130
Radius Increment
None
None
-0.1
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-5.5 (12,000,000 iterations)

 

[NEXT: Conclusions]

CONTENTS:

Index
Introduction
Methodology
Case Study of Aesthetic Forms
Conclusions