EUPHORIA

Crown functions at maximum amplitude. Kaleidoscopic symmetry. Stained glass tessellation at full saturation.

Maximum-amplitude functions, kaleidoscopic symmetry groups, crown waveforms, prismatic refraction, and stained glass tessellation. Systems at peak intensity — the mathematical ceiling.

50 renders. 5 survived.

Crown — f(θ) = |cos(nθ/2)|^{1/n}

Crown

f(θ) = |cos(nθ/2)|^{1/n}

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Firework — r(t) = v₀t - ½gt², θ ~ Uniform(0,2π)

Firework

r(t) = v₀t - ½gt², θ ~ Uniform(0,2π)

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Kaleidoscope — f(r,θ) = f(r, θ + 2π/n), n = 6

Kaleidoscope

f(r,θ) = f(r, θ + 2π/n), n = 6

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Prismatic — n(λ) = A + B/λ² + C/λ⁴

Prismatic

n(λ) = A + B/λ² + C/λ⁴

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Stained Glass — T(λ,x,y) = Σ cᵢ · χ_{Ωᵢ}(x,y) · S(λ)

Stained Glass

T(λ,x,y) = Σ cᵢ · χ_{Ωᵢ}(x,y) · S(λ)

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Complete EUPHORIA Series

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

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▶The Story Behind This Series

Euphoria is a system at maximum amplitude. It cannot go higher. The mathematics of extrema — peaks, crowns, saturated color fields — describe moments of maximum intensity. These are not sustainable states, which makes them precious.

Mathematical primitive: maximum amplitude, symmetry groups, tessellation, refraction