An Aesthetic Exploration of Relative Motions

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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: P_{0(x, y)} = (400, 300)

P₁: P_1(angle)= P_1(angle) + P_{1(angular
increment)}

P_1(x) = P_4(x) + P_1(radius) * P_{1(cos(angle))}

P_1(y) = P_4(y) + P_1(radius) * P_{1(sin(angle))}

P₂: P_2(angle) = P_2(angle) + P_{2(angular
increment)}

P_2(x) = P_3(x) + P_2(radius) * P_{2(cos(angle))}

P_2(y) = P_3(y) + P_2(radius) * P_{2(sin(angle))}

P₃: if P_3(radius)< 0 or P_{3(max radius)} > 120, then

set P_{3(radius increment)} to P_{3(radius increment)} * (-1)

end if

P_3(radius) = P_3(radius) + P_{3(radius increment)}

P_3(angle) = P_3(angle) + P_{3(angular increment)}

P_3(x) = P_0(x) + P_3(radius) * P_{3(cos(angle))}

P_3(y) = P_0(y) + P_3(radius) * P_{3(sin(angle))}

P₄: P_4(angle) = P_4(angle) + P_{4(angular
increment)}

P_4(x) = P_3(x) + P_4(radius) * P_{4(cos(angle))}

P_4(y) = P_3(y) + P_4(radius) * P_{4(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 P_3(y), then

set P_{1(angular increment)} to P_{1(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
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
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
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
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
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)

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CONTENTS:

Case Study of Aesthetic Forms