Spirals · 2D · v1.0.0
Fibonacci-Square Spiral
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Mathematics
Geometric construction
Squares with side lengths F₁…Fₙ placed counter-clockwise (right, up, left, down); a quarter-circle arc of radius Fₖ is drawn in each square. Scaled to fit 2R.
Symmetry: None; approximates the golden spiral as n grows.
Culture
Symbolic interpretation
Popular emblem of 'nature's code'; a mathematical approximation.
Formulas
Available frequency mappings
- A · Direct ratio fᵢ = f₀ · rᵢ
- B · Power fᵢ = f₀ · rᵢ^α
- C · Logarithmic fᵢ = f₀ · 2^(k · log₂ rᵢ)
- D · Reference distance fᵢ = f₀ · (dᵢ / d_ref)^α
- E · Angular rᵢ = θᵢ / θ_ref ; fᵢ = f₀ · rᵢ^α
Units u
Coordinates
| id | x | y | z |
|---|---|---|---|
| P0 | 0.2647 | 0.4118 | 0.0000 |
| P1 | 0.3235 | 0.4118 | 0.0000 |
| P2 | 0.3235 | 0.4706 | 0.0000 |
| P3 | 0.2647 | 0.4706 | 0.0000 |
| P4 | 0.3235 | 0.5294 | 0.0000 |
| P5 | 0.2647 | 0.5294 | 0.0000 |
| P6 | 0.1471 | 0.4118 | 0.0000 |
| P7 | 0.1471 | 0.5294 | 0.0000 |
| P8 | 0.1471 | 0.2353 | 0.0000 |
| P9 | 0.3235 | 0.2353 | 0.0000 |
| P10 | 0.6176 | 0.2353 | 0.0000 |
| P11 | 0.6176 | 0.5294 | 0.0000 |
| P12 | 0.6176 | 1.0000 | 0.0000 |
| P13 | 0.1471 | 1.0000 | 0.0000 |
| P14 | -0.6176 | 0.2353 | 0.0000 |
| P15 | -0.6176 | 1.0000 | 0.0000 |
| P16 | -0.6176 | -1.0000 | 0.0000 |
| P17 | 0.6176 | -1.0000 | 0.0000 |
Distances & angles
|P0P1|0.0588 u
|P1P2|0.0588 u
|P2P3|0.0588 u
|P3P0|0.0588 u
|P2P4|0.0588 u
|P4P5|0.0588 u
|P5P3|0.0588 u
|P6P0|0.1176 u
|P0P5|0.1176 u
|P5P7|0.1176 u
|P7P6|0.1176 u
|P8P9|0.1765 u
|P9P1|0.1765 u
|P1P6|0.1765 u
|P6P8|0.1765 u
|P9P10|0.2941 u
|P10P11|0.2941 u
|P11P4|0.2941 u
|P4P9|0.2941 u
|P7P11|0.4706 u
|P11P12|0.4706 u
|P12P13|0.4706 u
|P13P7|0.4706 u
|P14P8|0.7647 u
|P8P13|0.7647 u
|P13P15|0.7647 u
|P15P14|0.7647 u
|P16P17|1.2353 u
|P17P10|1.2353 u
|P10P14|1.2353 u
|P14P16|1.2353 u
∠P1P0P31.5708 rad
∠P1P0P63.1416 rad
∠P1P0P51.5708 rad
∠P3P0P61.5708 rad
∠P6P0P51.5708 rad
∠P0P1P21.5708 rad
∠P0P1P91.5708 rad
∠P2P1P93.1416 rad
∠P2P1P61.5708 rad
∠P9P1P61.5708 rad
∠P1P2P31.5708 rad
∠P1P2P43.1416 rad
∠P3P2P41.5708 rad
∠P2P3P01.5708 rad
∠P2P3P51.5708 rad
∠P0P3P53.1416 rad
∠P2P4P51.5708 rad
∠P2P4P111.5708 rad
∠P5P4P113.1416 rad
∠P5P4P91.5708 rad
∠P11P4P91.5708 rad
∠P4P5P31.5708 rad
∠P4P5P01.5708 rad
∠P4P5P73.1416 rad
∠P3P5P71.5708 rad
∠P0P5P71.5708 rad
∠P0P6P71.5708 rad
∠P0P6P81.5708 rad
∠P7P6P11.5708 rad
∠P7P6P83.1416 rad
∠P1P6P81.5708 rad
∠P5P7P61.5708 rad
∠P5P7P131.5708 rad
∠P6P7P111.5708 rad
∠P6P7P133.1416 rad
∠P11P7P131.5708 rad
∠P9P8P61.5708 rad
∠P9P8P143.1416 rad
∠P9P8P131.5708 rad
∠P6P8P141.5708 rad
∠P14P8P131.5708 rad
∠P8P9P11.5708 rad
∠P8P9P103.1416 rad
∠P8P9P41.5708 rad
∠P1P9P101.5708 rad
∠P10P9P41.5708 rad
∠P9P10P111.5708 rad
∠P9P10P171.5708 rad
∠P11P10P173.1416 rad
∠P11P10P141.5708 rad
∠P17P10P141.5708 rad
∠P10P11P41.5708 rad
∠P10P11P71.5708 rad
∠P10P11P123.1416 rad
∠P4P11P121.5708 rad
∠P7P11P121.5708 rad
∠P11P12P131.5708 rad
∠P12P13P71.5708 rad
∠P12P13P81.5708 rad
∠P12P13P153.1416 rad
∠P7P13P151.5708 rad
∠P8P13P151.5708 rad
∠P8P14P151.5708 rad
∠P8P14P161.5708 rad
∠P15P14P101.5708 rad
∠P15P14P163.1416 rad
∠P10P14P161.5708 rad
∠P13P15P141.5708 rad
∠P17P16P141.5708 rad
∠P16P17P101.5708 rad
Derived ratios
|P0P1|1.000000
∠P1P0P31.000000
|P6P0|2.000000
∠P1P0P62.000000
|P9P1|3.000000
|P9P10|5.000000
|P7P11|8.000000
|P8P13|13.000000
|P16P17|21.000000
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