Turtle Geometry No 2
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Turtle Geometry No 2
Turtle geometry is applied to create different kinds of beautiful symmetric objects looking like stars or snowflakes. The change of inclination angles of lines follows some prescribed rules. Lines are combined with special functions to generate colorful surroundings.
Formula
- \varphi_{i+1} = \varphi_i + 36° \cdot i^4-180°
Turtle Object No 45
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 72° \cdot i^4-180°
Turtle Object No 46
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 108° \cdot i^4-180°
Turtle Object No 47
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 30° \cdot i^4-180°
Turtle Object No 48
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 150° \cdot i^4-180°
Turtle Object No 49
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 11.25° \cdot i^4-180°
Turtle Object No 50
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 10° \cdot i^4-180°
Turtle Object No 51
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 9° \cdot i^4-180°
Turtle Object No 52
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 4.5° \cdot i^4-180°
Turtle Object No 53
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 31.5° \cdot i^4-180°
Turtle Object No 54
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 58.5° \cdot i^4-180°
Turtle Object No 55
Licence CC BY-NC-SA-3.0
Turtle Object No 56
Licence CC BY-NC-SA-3.0
Turtle Object No 57
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 3.75° \cdot i^4-180°
Turtle Object No 58
Licence CC BY-NC-SA-3.0
Turtle Object No 59
Licence CC BY-NC-SA-3.0
Turtle Object No 60
Licence CC BY-NC-SA-3.0
Turtle Object No 61
Licence CC BY-NC-SA-3.0
Turtle Object No 62
Licence CC BY-NC-SA-3.0
Turtle Object No 63
Licence CC BY-NC-SA-3.0
Turtle Object No 64
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 20° \cdot \left( i^2 + i^4 \right) -180°
Turtle Object No 65
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 18° \cdot \left( i^2 + i^4 \right) -180°
Turtle Object No 66
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 18° \cdot \left( 2i^2 + i^4 \right) -180°
Turtle Object No 67
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 10° \cdot \left( i^2 + i^4 \right) -180°
Turtle Object No 68
Licence CC BY-NC-SA-3.0
Formula
- \varphi_{i+1} = \varphi_i + 9° \cdot \left( i^2 + i^4 \right) -180°
Turtle Object No 69
Licence CC BY-NC-SA-3.0
Turtle Object No 70
Licence CC BY-NC-SA-3.0
