An Aesthetic Exploration of Relative Motions

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3. Case Study of Aesthetic Forms

3-1 Multiple-level Relative Motions

Figure 3-1 Motions Illustration

Rules:

P₀: P_0(x,y) = (0, 0)

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_5(x)+ P_2(radius)* P_{2(cos(angle))}

P_2(y) = P_5(y)+ P_2(radius)* P_{2(sin(angle))}

P₃: 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(x,y) = (P_2(x,y)+ P_3(x,y)) / 2

P₅: P_5(x,y) = (P_1(x,y)+ P_3(x,y)) / 2

P₆: P_6(x,y) = (P_1(x,y)+ P_2(x,y)+ P_3(x,y)) / 3

Trajectory Recorded: P₆

Table: Case 3-1.1 Parameters Assigned (Figure 3-1.1)

Point	P₁	P₂	P₃
Coordinate System	P₄	P₅	P₀
Initial Angle	180	0	0
Angular Increment	0.1300	-0.3900	0.1203
Radius(pixel)	150	110	80
Radius Increment	None	None	None

* Positive angle means clockwise rotation, negative counterclockwise.

[Enlarge the image]

Figure 3-1.1 (12,000,000 iterations)

Table: Case 3-1.2 Parameters Assigned (Figure 3-1.2)

Point	P₁	P₂	P₃
Coordinate System	P₄	P₅	P₀
Initial Angle	0	0	0
Angular Increment	0.1300	-0.3900	0.1203
Radius(pixel)	150	150	80
Radius Increment	None	None	None

* Positive angle means clockwise rotation, negative counterclockwise.

[Enlarge the image]

Figure 3-1.2 (12,000,000 iterations)

Table: Case 3-1.3 Parameters Assigned (Figure 3-1.3)

Point	P₁	P₂	P₃
Coordinate System	P₄	P₅	P₀
Initial Angle	0	0	0
Angular Increment	-0.16003	0.48141	-0.04009
Radius(pixel)	150	150	60
Radius Increment	None	None	None

* Positive angle means clockwise rotation, negative counterclockwise.

[Enlarge the image]

Figure 3-1.3 (12,000,000 iterations)

Table: Case 3-1.4 Parameters Assigned (Figure 3-1.4)

Point	P₁	P₂	P₃
Coordinate System	P₄	P₅	P₀
Initial Angle	0	0	0
Angular Increment	-0.16003	0.48141	-0.00100
Radius(pixel)	150	150	60
Radius Increment	None	None	None

* Positive angle means clockwise rotation, negative counterclockwise.

[Enlarge the image]

Figure 3-1.4 (12,000,000 iterations)

Table: Case 3-1.5 Parameters Assigned (Figure 3-1.5)

Point	P₁	P₂	P₃
Coordinate System	P₄	P₅	P₀
Initial Angle	0	0	180
Angular Increment	0.36003	-0.24000	0.16
Radius(pixel)	120	180	60
Radius Increment	None	None	None

* Positive angle means clockwise rotation, negative counterclockwise.

[Enlarge the image]

Figure 3-1.5 (85,200 iterations)

Table: Case 3-1.6 Parameters Assigned (Figure 3-1.6)

Point	P₁	P₂	P₃
Coordinate System	P₄	P₅	P₀
Initial Angle	0	0	180
Angular Increment	-1.2003	0.51	0.15
Radius(pixel)	120	180	60
Radius Increment	None	None	None

* Positive angle means clockwise rotation, negative counterclockwise.

[Enlarge the image]

Figure 3-1.6 (270,000 iterations)

Table: Case 3-1.7 Parameters Assigned (Figure 3-1.7)

Point	P₁	P₂	P₃
Coordinate System	P₄	P₅	P₀
Initial Angle	0	90	0
Angular Increment	0.18	-0.24	-0.4207
Radius(pixel)	160	120	80
Radius Increment	None	None	None

* Positive angle means clockwise rotation, negative counterclockwise.

[Enlarge the image]

Figure 3-1.7 (521,700 iterations)

Table: Case 3-1.8 Parameters Assigned (Figure 3-1.8)

Point	P₁	P₂	P₃
Coordinate System	P₄	P₅	P₀
Initial Angle	0	90	0
Angular Increment	0.21	0.3509	-0.49
Radius(pixel)	200	40	90
Radius Increment	None	None	None

* Positive angle means clockwise rotation, negative counterclockwise.

[Enlarge the image]

Figure 3-1.8 (148,200 iterations)

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Case Study of Aesthetic Forms