FRACTURED

Piecewise functions where the limit from the left never meets the limit from the right. The discontinuity is the emotion.

Piecewise discontinuous functions rendered as visual fields. Each piece explores a different topology of breaking — bifurcation cascades, catastrophe folds, Voronoi shattering, seismic faults, glass fracture networks. The mathematics of rupture made visible.

47 renders. 5 survived.

Bifurcation — x_{n+1} = rx_n(1 - x_n)

Bifurcation

x_{n+1} = rx_n(1 - x_n)

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Catastrophe Fold — V(x) = x⁴ + ax² + bx

Catastrophe Fold

V(x) = x⁴ + ax² + bx

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Glass Fracture — K_I = σ√(πa)

Glass Fracture

K_I = σ√(πa)

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Seismic Fault — log₁₀(N) = a - bM

Seismic Fault

log₁₀(N) = a - bM

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Voronoi Shatter — V(p) = {x : d(x,p) ≤ d(x,q) ∀q}

Voronoi Shatter

V(p) = {x : d(x,p) ≤ d(x,q) ∀q}

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Complete FRACTURED Series

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

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▶The Story Behind This Series

Fracture is not random. When a material breaks, it follows the physics of stress propagation. When a life breaks, it follows the topology of connection — the pieces that were closest fracture first. This series uses discontinuous functions, bifurcation diagrams, and Voronoi tessellation to map the geometry of things coming apart.

Mathematical primitive: piecewise discontinuous functions, bifurcation, Voronoi tessellation