## 3. Case Study of Aesthetic Forms

### 3-2 Chaotic Multiple-level Relative Motions

 Figure 3-2 Motions Illustration Rules: dAP3 = Constant (*dAP3: dynamic angular increment of Point P3) P0: P0(x,y) = (0, 0) 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) = P5(x) + P2(radius) * P2(cos(angle))         P2(y) = P5(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)) P4: P4(x,y) = (P2(x,y) + P3(x,y)) / 2 P5: P5(x,y) = (P1(x,y) + P3(x,y)) / 2 P6: P6(x,y) = (P1(x,y) + P2(x,y) + P3(x,y)) / 3 Trajectory Recorded: P6

Table: Case 3-2.1 Parameters Assigned (Figure 3-2.1)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 0 0 Angular Increment 0.04 -0.36 ceiling limit: 0.42 floor limit: 0.24 Radius(pixel) 150 150 80 Radius Increment None None None Chaotic Terms if P3(y) is greater than or equal to P6(y), then      if P3(angular increment) >= dAP3(ceiling limit) or P3(angular increment) <=      dAP3(floor limit), then      set dAP3 to dAP3 * (-1)      end if      P3(angular increment) = P3(angular increment) + dAP3 end if
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Figure 3-2.1 (12,000,000 iterations)

dAP3 = 0.00031
* Positive angle means clockwise rotation, negative counterclockwise.

Table: Case 3-2.2 Parameters Assigned (Figure 3-2.2)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 180 0 0 Angular Increment 0.32 0.24 ceiling limit: 0.42 floor limit: -0.48 Radius(pixel) 150 150 80 Radius Increment None None None Chaotic Terms if P3(y) is greater than or equal to P6(y), then      if P3(angular increment) >= dAP3(ceiling limit) or P3(angular increment) <=      dAP3(floor limit), then      set dAP3 to dAP3 * (-1)      end if      P3(angular increment) = P3(angular increment) + dAP3 else if P3(y) is less than P6(y), then      set P3(angular increment) to P3(angular increment) * (-1) end if
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Figure 3-2.2 (12,000,000 iterations)

dAP3 = 0.003
* Positive angle means clockwise rotation, negative counterclockwise.

Table: Case 3-2.3 Parameters Assigned (Figure 3-2.3)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle -180 0 0 Angular Increment 0.32 0.24 ceiling limit: 0.82 floor limit: -0.48 Radius(pixel) 150 100 80 Radius Increment None None None Chaotic Terms if P3(y) is greater than or equal to P6(y), then      if P3(angular increment) >= dAP3(ceiling limit) or P3(angular increment) <=      dAP3(floor limit), then      set dAP3 to dAP3 * (-1)      end if      P3(angular increment) = P3(angular increment) + dAP3 else if P3(y) is less than P6(y), then      set P3(angular increment) to P3(angular increment) * (-1) end if
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Figure 3-2.3 (12,000,000 iterations)

dAP3 = 0.007
* Positive angle means clockwise rotation, negative counterclockwise.

Table: Case 3-2.4 Parameters Assigned (Figure 3-2.4)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 0 0 Angular Increment -0.16 0.24 ceiling limit: 0.560036 floor limit: -0.480700 Radius(pixel) 240 120 60 Radius Increment None None None Chaotic Terms if P3(y) is greater than or equal to P6(y), then      set P3(angular increment) to P3(angular increment) * (-1) else if P3(y) is less than P6(y), then      if P3(angular increment) >= dAP3(ceiling limit) or P3(angular increment) <=      dAP3(floor limit), then      set dAP3 to dAP3 * (-1)      end if      P3(angular increment) = P3(angular increment) + dAP3 end if
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Figure 3-2.4 (12,000,000 iterations)

dAP3 = 0.023
* Positive angle means clockwise rotation, negative counterclockwise.

Table: Case 3-2.5 Parameters Assigned (Figure 3-2.5)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 0 0 Angular Increment 0.2 -0.24 ceiling limit: 0.160036 floor limit: -0.480700 Radius(pixel) 240 120 60 Radius Increment None None None Chaotic Terms if P3(y) is greater than or equal to P6(y), then      set P3(angular increment) to P3(angular increment) * (-1) else if P3(y) is less than P6(y), then      if P3(angular increment) >= dAP3(ceiling limit) or P3(angular increment) <=      dAP3(floor limit), then      set dAP3 to dAP3 * (-1)      end if      P3(angular increment) = P3(angular increment) + dAP3 end if
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Figure 3-2.5 (12,000,000 iterations)

dAP3 = 0.004
* Positive angle means clockwise rotation, negative counterclockwise.

Table: Case 3-2.6 Parameters Assigned (Figure 3-2.6)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 0 0 Angular Increment 0.18 -0.24 ceiling limit: 0.240036 floor limit: -0.480700 Radius(pixel) 240 120 60 Radius Increment None None None Chaotic Terms if P3(y) is greater than or equal to P6(y), then      set P3(angular increment) to P3(angular increment) * (-1) else if P3(y) is less than P6(y), then      if P3(angular increment) >= dAP3(ceiling limit) or P3(angular increment) <=      dAP3(floor limit), then      set dAP3 to dAP3 * (-1)      end if      P3(angular increment) = P3(angular increment) + dAP3 end if
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Figure 3-2.6 (12,000,000 iterations)

dAP3 = 0.004
* Positive angle means clockwise rotation, negative counterclockwise.

Table: Case 3-2.7 Parameters Assigned (Figure 3-2.7)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 0 0 Angular Increment -0.24 ceiling limit: 0.18 ceiling limit: 0.48 floor limit: 0.12 floor limit: 0.26 Radius(pixel) 150 150 80 Radius Increment None None None Chaotic Terms P2:  if P2(angular increment) >= dAP2(ceiling limit) or P2(angular increment) <=      dAP2(floor limit), then      set dAP2 to dAP2 * (-1) end if P3: if P3(y) is less than P6(y), then      if P3(angular increment) >= dAP3(ceiling limit) or P3(angular increment) <=      dAP3(floor limit), then      set dAP3 to dAP3 * (-1)      end if      P3(angular increment) = P3(angular increment) + dAP3 end if
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Figure 3-2.7 (12,000,000 iterations)

dAP2 = -0.003
dAP3 = -0.008
* Positive angle means clockwise rotation, negative counterclockwise.

CONTENTS:

 Index Introduction Methodology Case Study of Aesthetic Forms Conclusions