Singularity
Coupled Oscillators
Void
Attractors
Loom
Strange Attractor
Pursuit
Reaction Diffusion

The geometry of feeling.

f(z) = 1/(z-z₀)ⁿ, n ≥ 1

Mathematical fine art for people who think precisely and feel deeply.

Every piece begins with a human emotion — grief, growth, connection — and asks: what mathematical function has the same shape as this feeling? We researched that emotion across art history and science, then built the image from first principles. The equation isn't decoration. It's the reason the piece looks the way it does.

In a world of AI-generated imagery, we went the other direction. This is minimalist fine art built from mathematical first principles — not prompted, not generated, not automated. Every curve was chosen. Every parameter was earned.

Built in Python. Evaluated as art. Not AI-generated.

AWE

Cathedral proportions. Chladni patterns appearing from vibration. Singularities where the mathematics breaks down.

Cathedral — h(x) = Σ Aₙ sin(nπx/L), n → ∞

Cathedral

Chladni — ∇⁴w - k⁴w = 0

Chladni

Monolith — f(x,y) = H(x-a)H(b-x)H(y-c)H(d-y)

Monolith

Radiance — L(x,ω) = Lₑ + ∫ f_r L_i cos θ dω

Radiance

Singularity — f(z) = 1/(z-z₀)ⁿ, n ≥ 1

Singularity

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CONNECTION

Two parametric curves with a phase offset. Neither leads nor follows. The gap between them is the relationship.

Coupled Oscillators — ẍ₁ = -ω₁²x₁ + κ(x₂ - x₁)

Coupled Oscillators

Double Helix — r(t) = (cos t, sin t, t/2π) ± d/2

Double Helix

Phase Sync — dθ/dt = ω + K sin(θ₂ - θ₁)

Phase Sync

Torus Knot — r(t) = ((R + r cos qt) cos pt, ...)

Torus Knot

Two Body — F = -Gm₁m₂/r² · r̂

Two Body

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OVERWHELM

Twelve harmonics, eight wave sources, twenty-two parallel streams. Each coherent alone. Together, unresolvable.

Attractors — dx/dt = σ(y-x), dy/dt = x(ρ-z)-y

Attractors

Kuramoto — dθᵢ/dt = ωᵢ + (K/N)Σsin(θⱼ - θᵢ)

Kuramoto

Levy Swarm — P(x) ~ |x|^{-1-α}, 0 < α < 2

Levy Swarm

Phase Flood — ψ(x,t) = Σ Aₙ e^{i(kₙx - ωₙt + φₙ)}

Phase Flood

Turbulence — Re = ρvL/μ >> Re_cr

Turbulence

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GRIEF

Exponential decay toward zero. Half-life curves draining from two directions. The plateau that holds until the edges yield.

Heat Diffusion — ∂u/∂t = α∇²u

Heat Diffusion

Heaviside Cascade — H(t - t₀) = {0, t < t₀; 1, t ≥ t₀}

Heaviside Cascade

Spectral Erosion — S(f,t) = S₀(f) · e^{-γ(f)t}

Spectral Erosion

Void — ∫∫ ρ(x,y) dA → 0

Void

Weight — F = mg, m(t) = m₀(1 - e^{-t/τ})

Weight

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SURRENDER

Terminal velocity. Dissolution into equilibrium. The mathematics of ceasing to resist.

Dissolution — dm/dt = -kA(c_s - c)

Dissolution

Flow — ∇·v = 0, Re << 1

Flow

Melt — ρL(ds/dt) = k(∂T/∂n)

Melt

Settle — v_t = (2r²(ρ_p - ρ_f)g)/(9μ)

Settle

Shed — f(t) = f₀ · H(t₀ - t)

Shed

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DESIRE

Gravitational inspiral. Pursuit curves that never close. The asymptote you cannot reach but cannot stop approaching.

Eclipse — I(r) = I₀ · (1 - disk(r/R))

Eclipse

Flame — ∂T/∂t = α∇²T + Q(x,y)

Flame

Hunger — dN/dt = rN(1 - N/K) - aN/(1+bN)

Hunger

Inspiral — r(t) = r₀(1 - t/t_c)^{1/4}

Inspiral

Pursuit — dr/dt = v₁ · (r_target - r)/||r_target - r||

Pursuit

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CYCLES

Phase portraits closing on themselves. Möbius strips with no beginning. Orbits that always return to where they started.

Loom — x(t) = x(t + T), T = 2π/ω

Loom

Moebius — r(t) = ((2 + cos(t/2))cos t, (2 + cos(t/2))sin t, sin(t/2))

Moebius

Orbit — r(θ) = a(1-e²)/(1 + e cos θ)

Orbit

Phase Portrait — ẋ = f(x,y), ẏ = g(x,y)

Phase Portrait

Recurrence — R(i,j) = Θ(ε - ||x_i - x_j||)

Recurrence

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SOLITUDE

One point in an infinite plane. One signal in silence. The mathematics of being the only thing present.

Echo — f(t - τ) · α^n, α < 1

Echo

Footprints — δ(x - x_n), n = 1,2,...,N

Footprints

Island — Ω = {x : f(x) > 0} ⊂ R², |∂Ω| < ∞

Island

Lighthouse — I(r) = I₀/r² · rect(θ/Δθ)

Lighthouse

Wanderer — x(t) = x₀ + ∫₀ᵗ v(s)ds, v random

Wanderer

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PEACE

Laplacian steady state. Resolved harmonics. Sand settling into the shape the wind intended.

Cloud — ∂ρ/∂t = 0, ∇·(ρv) = 0

Cloud

Resolved — ∇²f = 0

Resolved

Sand — ∂h/∂t = ν∇²h - λ(∇h)² + η

Sand

Settled — v(t) → 0, x(t) → x_eq

Settled

Zen Garden — ψ = A · sin(kx) · sin(ky)

Zen Garden

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NOSTALGIA

Low-pass filtered memories. Daguerreotype decay. Music box harmonics winding down.

Carousel — r(t) = R · e^{iωt}, ω → 0

Carousel

Daguerreotype — I(x,y,t) = I₀(x,y) · e^{-t/τ} + η(x,y)

Daguerreotype

Locket — f(x) = f₀(x) * g(σ), σ → ∞

Locket

Music Box — x(t) = Σ Aₙe^{-γₙt}sin(nωt)

Music Box

Remnant — R(x) = lim_{t→∞} f(x,t)

Remnant

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