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 → ∞

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

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

Cathedral

Chladni

Monolith

Radiance

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)

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

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

Coupled Oscillators

Double Helix

Phase Sync

Torus Knot

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

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

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

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

Attractors

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

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GRIEF

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

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

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

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

Heat Diffusion

Heaviside Cascade

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

Spectral Erosion

Void

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

Weight

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GROWTH

L-system branching at thirteen levels. Golden spirals tiling the plane. Thirty-four lines reaching toward light.

$Bifurcation — x_{n+1} = rx_n(1 - x_n), r ∈ [2.5, 4]$

Lissajous Bloom — x = A sin(at + δ), y = B sin(bt)

Reaction Diffusion — ∂u/∂t = Dᵤ∇²u + f(u,v)

$Bifurcation — x_{n+1} = rx_n(1 - x_n), r ∈ [2.5, 4]$

Bifurcation

Dendrite

Lissajous Bloom

Logistic Cascade

Reaction Diffusion

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DESIRE

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

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

$Inspiral — r(t) = r₀(1 - t/t_c)^{1/4}$

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

Eclipse

Flame

Hunger

$Inspiral — r(t) = r₀(1 - t/t_c)^{1/4}$

Inspiral

Pursuit

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CYCLES

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

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

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

Loom

Moebius

Orbit

Phase Portrait

Recurrence

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SOLITUDE

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

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

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

Echo

Footprints

Island

Lighthouse

Wanderer

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WONDER

Apollonian gaskets, strange attractors, recursive depth. The mathematics that makes you stop and stare.

Apollonian Gasket — (k₁+k₂+k₃+k₄)² = 2(k₁²+k₂²+k₃²+k₄²)

$Harmonograph — x = A₁sin(f₁t+φ₁)e^{-d₁t} + A₂sin(f₂t+φ₂)e^{-d₂t}$

$Mandelbrot Orbit — z_{n+1} = z_n² + c$

Strange Attractor — dx/dt = σ(y-x), dy/dt = x(ρ-z)-y, dz/dt = xy-βz

Apollonian Gasket

$Harmonograph — x = A₁sin(f₁t+φ₁)e^{-d₁t} + A₂sin(f₂t+φ₂)e^{-d₂t}$

Harmonograph

$Mandelbrot Orbit — z_{n+1} = z_n² + c$

Mandelbrot Orbit

Recursion

Strange Attractor

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NOSTALGIA

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

$Carousel — r(t) = R · e^{iωt}, ω → 0$

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

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

$Remnant — R(x) = lim_{t→∞} f(x,t)$

$Carousel — r(t) = R · e^{iωt}, ω → 0$

Carousel

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

Daguerreotype

Locket

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

Music Box

$Remnant — R(x) = lim_{t→∞} f(x,t)$

Remnant

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