Foundation / Configurator
Parametric Design Tool

Parametric design configurator.

Pick a hardware design class, set your parameters, and receive the complete φ-derived specification — every dimension, ratio, and material determined by the framework with zero free parameters.

Mode(r, s, k, t) — Four integers, one identity, complete bearing. Every dimension derives from φ²=φ+1. The groove conformity f(k) = (φᵏ+φ⁻ᵏ)/2 generates Lucas numbers at even k and √5·Fibonacci at odd k.

INPUT 1 — BORE LEVEL n
L1 WatchmakingL10 Ship propulsion
Level 5 — bore ø35.89 mm — Motors/Aero
INPUT 2 — WIDTH SERIES s
INPUT 3 — GROOVE CLASS k
INPUT 4 — MATERIAL TIER t

L = π(1−ζ) · M · r⁴ — Two inputs, complete gyroscope. Specify angular momentum and material tier. The math delivers the complete gyroscope — every bearing dimension, rotor, housing, motor, and RPM — from φ²=φ+1 with zero free parameters.

INPUT 1 — ANGULAR MOMENTUM
10 µN·m·s10,000 N·m·s
0.500 N·m·s
INPUT 2 — MATERIAL TIER

φCoherent Tri-Lobed Impeller Disc. Radial φ-cascade: D → D/φ² → D/φ⁴. Axial √5-cascade: H = D/(√5·φ²). Lobe span 120°/φ = 74.16° · Channel 120°/φ² = 45.84°. Bowl slope arctan(2/(√5·φ²)) = 18.86°. The F(15) instance is the Sabu Disc of Egypt, c. 3000 BCE.

INPUT 1 — FIBONACCI LEVEL n
F(5) = 5 mmF(17) = 1597 mm
F(13) = 233 mm — Industrial circulation
INPUT 2 — MATERIAL TIER

Seven φ-Identities · Any Fluid · Any Scale. Select a working medium and Fibonacci level. All seven fluid dynamics identities update live after generation. Dimensionless ratios are identical across all media — only absolute magnitudes change.

WORKING MEDIUM
TERRESTRIAL
SPACE APPLICATIONS
FIBONACCI LEVEL F(n)
F(10)=55mm MicroF(20)=6765mm Marine
F(14) = 377 mm — Process pump

φCoherent Hydraulic Ram Pump. Drive pipe L/D = φ³ · Efficiency η = 1/φ · Cascade amplification φᴺ. Water hammer in a Fibonacci-proportioned pipe delivers fluid to arbitrary head with no external power. Every dimension from φ²=φ+1.

FIBONACCI LEVEL n
55mm garden1597mm civil
F(14) = 377 mm
SUPPLY HEAD
3 m50 m
15 m supply head
CASCADE STAGES N
N=1 · φ×N=9 · φ⁹×
3 stages · φ³ = 4.236×
MATERIAL TIER

φCoherent Dual-Function Nozzle. Forward thrust: vane angle arctan(1/φ) = 31.717° · area ratio 1/(2φ) · 3-sector exit. Two material branches from φ²=φ+1: Fibonacci composite (Al-Sc-Se) for forward thrust vanes · Lucas cermet (Cu-Ag-Os) for extreme/acoustic service.

FIBONACCI LEVEL n — INLET Dₙ = F(n) mm
F(10) = 55 mmF(15) = 610 mm
F(13) = 233 mm
MATERIAL BRANCH — VANE COMPOSITION

Proof-of-concept of the φCoherent Cellular Framework. Three cell types tile in a golden-angle spiral. Every 13 cells form a self-contained supercluster (8:5 ≈ φ). Population grows as the Fibonacci sequence. All dimensions derive from S = λ₈/φ⁵ = 613.67 mm.

CITY GROWTH — GOLDEN-ANGLE PHYLLOTAXIS
1 supercluster (13 cells)350 SC (19M people)
1 supercluster · 8 living + 3 industrial + 2 agricultural
● Residential (837m) ● Commercial (320m) ● Industrial (1,354m) ● Agricultural (2,191m) ● Education (198m) ● Health (518m)
—
Population
—
Total cells
—
City diameter
—
Area (km²)
—
Air transit (min)
—
Lev-rail (min)
CELL BREAKDOWN
TRANSPORT SPIRAL ARMS
SUBSURFACE SPINE CROSS-SECTION
SINGLE-CELL INTERNAL ZONING — LUCAS 9:6:3
Unique Lucas-coherent ternary partition (proved by exhaustion). 9+6+3=L(6)=18=Ar.
LUCAS CONDUCTOR PALETTE — L(n)=φⁿ+ψⁿ
L(n)ElementRoleψⁿGap
Key identity: L(n+1)−L(n)=L(n−1). Closure: L(10)=123 > Z=118. Hierarchy terminates.
INFRASTRUCTURE DIMENSIONS — ALL FROM S = λ₈/φ⁵ = 613.67 mm
ComponentExpressionDimension
FIBONACCI GROWTH PROGRESSION
SuperclustersCellsPopulationDiameterAir timeLev routes
DERIVATION CHAIN — EVERY DIMENSION FROM φ²=φ+1
φ²=φ+1 → Q=φ → f₈=49.958 Hz → λ₈=6,806 mm → S=λ₈/φ⁵=613.67 mm
S×φ¹⁵=837m living · S×φ¹⁶=1,354m industrial · S×φ¹⁷=2,191m agricultural
Cell pop=F(20)=6,765 · Supercluster=F(8)=21 (13:8≈φ, 6 types) · Full city=F(37)=24,157,817 · Zero free parameters