PRIDE

Golden ratio proportions. Spires rising to computed vertices. The mathematics of earned height.

Golden ratio geometry, spire functions, crown curves, flourish dynamics, and unfurling sequences. Systems that have earned their height and display it with structural integrity.

43 renders. 5 survived.

Crown — r(θ) = 1 + ε·cos(nθ), n ≥ 5

Crown

r(θ) = 1 + ε·cos(nθ), n ≥ 5

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Flourish — γ(t) = (t·cos(t), t·sin(t), t²)

Flourish

γ(t) = (t·cos(t), t·sin(t), t²)

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Golden Ratio — φ = (1 + √5)/2 ≈ 1.618...

Golden Ratio

φ = (1 + √5)/2 ≈ 1.618...

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Spire — h(x) = H · (1 - |x/w|^p)^{1/p}

Spire

h(x) = H · (1 - |x/w|^p)^{1/p}

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Unfurl — θ(t) = θ₀ + (π - θ₀)(1 - e^{-t/τ})

Unfurl

θ(t) = θ₀ + (π - θ₀)(1 - e^{-t/τ})

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Complete PRIDE Series

All 5 pieces as high-resolution PDFs. Print-ready at 300 DPI.

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▶The Story Behind This Series

Pride is vertical. The mathematics of pride involves height, proportion, and the golden ratio — the ratio that appears in architecture, nature, and art whenever a structure achieves a proportion that feels earned rather than forced.

Mathematical primitive: golden ratio, vertical growth, proportioned structure