Circle-based · 2D · v1.0.0
Fruit of Life
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Mathematics
Geometric construction
13 circles of radius R: one at the origin, six at distance 2R and six at distance 4R along the same six directions (60° apart).
Symmetry: Dihedral D6.
Culture
Symbolic interpretation
Described in modern sacred-geometry literature as a hidden pattern within the Flower of Life.
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 | 0.0000 | 0.0000 | 0.0000 |
| P1 | 0.0000 | 1.0000 | 0.0000 |
| P2 | -0.8660 | 0.5000 | 0.0000 |
| P3 | -0.8660 | -0.5000 | 0.0000 |
| P4 | -0.0000 | -1.0000 | 0.0000 |
| P5 | 0.8660 | -0.5000 | 0.0000 |
| P6 | 0.8660 | 0.5000 | 0.0000 |
| P7 | 0.0000 | 2.0000 | 0.0000 |
| P8 | -1.7321 | 1.0000 | 0.0000 |
| P9 | -1.7321 | -1.0000 | 0.0000 |
| P10 | -0.0000 | -2.0000 | 0.0000 |
| P11 | 1.7321 | -1.0000 | 0.0000 |
| P12 | 1.7321 | 1.0000 | 0.0000 |
Distances & angles
r(C0)0.5000 u
r(C1)0.5000 u
r(C2)0.5000 u
r(C3)0.5000 u
r(C4)0.5000 u
r(C5)0.5000 u
r(C6)0.5000 u
r(C7)0.5000 u
r(C8)0.5000 u
r(C9)0.5000 u
r(C10)0.5000 u
r(C11)0.5000 u
r(C12)0.5000 u
|C0C1|1.0000 u
|C0C2|1.0000 u
|C0C3|1.0000 u
|C0C4|1.0000 u
|C0C5|1.0000 u
|C0C6|1.0000 u
|C0C7|2.0000 u
|C0C8|2.0000 u
|C0C9|2.0000 u
|C0C10|2.0000 u
|C0C11|2.0000 u
|C0C12|2.0000 u
|C1C2|1.0000 u
|C1C3|1.7321 u
|C1C4|2.0000 u
|C1C5|1.7321 u
|C1C6|1.0000 u
|C1C7|1.0000 u
|C1C8|1.7321 u
|C1C9|2.6458 u
|C1C10|3.0000 u
|C1C11|2.6458 u
|C1C12|1.7321 u
|C2C3|1.0000 u
|C2C4|1.7321 u
|C2C5|2.0000 u
|C2C6|1.7321 u
|C2C7|1.7321 u
|C2C8|1.0000 u
|C2C9|1.7321 u
|C2C10|2.6458 u
|C2C11|3.0000 u
|C2C12|2.6458 u
|C3C4|1.0000 u
|C3C5|1.7321 u
|C3C6|2.0000 u
|C3C7|2.6458 u
|C3C8|1.7321 u
|C3C9|1.0000 u
|C3C10|1.7321 u
|C3C11|2.6458 u
|C3C12|3.0000 u
|C4C5|1.0000 u
|C4C6|1.7321 u
|C4C7|3.0000 u
|C4C8|2.6458 u
|C4C9|1.7321 u
|C4C10|1.0000 u
|C4C11|1.7321 u
|C4C12|2.6458 u
|C5C6|1.0000 u
|C5C7|2.6458 u
|C5C8|3.0000 u
|C5C9|2.6458 u
|C5C10|1.7321 u
|C5C11|1.0000 u
|C5C12|1.7321 u
|C6C7|1.7321 u
|C6C8|2.6458 u
|C6C9|3.0000 u
|C6C10|2.6458 u
|C6C11|1.7321 u
|C6C12|1.0000 u
|C7C8|2.0000 u
|C7C9|3.4641 u
|C7C10|4.0000 u
|C7C11|3.4641 u
|C7C12|2.0000 u
|C8C9|2.0000 u
|C8C10|3.4641 u
|C8C11|4.0000 u
|C8C12|3.4641 u
|C9C10|2.0000 u
|C9C11|3.4641 u
|C9C12|4.0000 u
|C10C11|2.0000 u
|C10C12|3.4641 u
|C11C12|2.0000 u
Derived ratios
r(C0)1.000000
|C4C5|2.000000
|C1C8|3.464102
|C10C11|4.000000
|C2C12|5.291503
|C6C9|6.000000
|C7C9|6.928203
|C7C10|8.000000
f_i = f_0 × r_i · v1.0.0 · user-configured
Frequency derivation — centre distances
| id | r = d / R | exact (reference) | sources | f = f₀ × r |
|---|---|---|---|---|
| R1 | 2.000000000 | 2 | |P0P1| |P0P2| |P0P3| … | 220 × 2 = 440.000 Hz |
| R2 | 3.464101615 | 2√3 | |P1P3| |P1P5| |P1P8| … | 220 × 2√3 = 762.102 Hz |
| R3 | 4.000000000 | 4 | |P0P7| |P0P8| |P0P9| … | 220 × 4 = 880.000 Hz |
| R4 | 5.291502622 | 2√7 | |P1P9| |P1P11| |P2P10| … | 220 × 2√7 = 1164.131 Hz |
| R5 | 6.000000000 | 6 | |P1P10| |P2P11| |P3P12| … | 220 × 6 = 1320.000 Hz |
| R6 | 6.928203230 | 4√3 | |P7P9| |P7P11| |P8P10| … | 220 × 4√3 = 1524.205 Hz |
| R7 | 8.000000000 | 8 | |P7P10| |P8P11| |P9P12| | 220 × 8 = 1760.000 Hz |
Click a row to highlight its source points in the drawing. R = 0.5000 u. Exact forms are recognised reference values; the calculation itself is numeric. This mapping is a chosen design rule, not a law of nature.
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