Turing Coral — Turing Patterns mathematical physical art

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Turing Coral

Turing Patterns

Labyrinthine patterns reminiscent of brain coral and organic mazes.

Price

$29.00

Shipping calculated at checkout

Format Art Print
Size 18 × 24 in
Material Enhanced matte paper · 200gsm · archival · unframed
Resolution 300 DPI · rendered at 5400 × 7200 px
Production Professional print-on-demand · ships from nearest facility
Shipping Most countries · calculated at checkout
Shipping & Delivery ⌄

Each print is produced and shipped from the nearest facility in our global print network. Production normally takes 2–5 business days, then shipping follows Printful's live estimate for the destination. The ranges below are current standard-rate estimates and can vary by exact address, product, and carrier availability.

Standard US 3–6 days · EU 3–15 days · Asia/Pacific 2–17 days · LatAm 5–25 days
Express Availability varies by product and destination
RegionCountriesEst. delivery
United States All 50 states + territories 3 – 6 business days
United Kingdom UK 2 – 11 business days
Canada Canada 2 – 10 business days
Australia Australia, New Zealand 3 – 17 business days
European Union Germany, France, Spain, Italy, Netherlands, Belgium, Austria, Sweden, Poland, Denmark, Finland, Ireland, Portugal, Czech Republic, Romania, Greece + more 3 – 15 business days
Norway & Switzerland NO, CH 3 – 15 business days
Latin America Brazil, Mexico, Chile, Colombia, Argentina, Peru + more 5 – 25 business days
Asia Pacific Japan, South Korea, Singapore, India, China, Hong Kong, Taiwan, Malaysia, Thailand, Philippines + more 2 – 20 business days
Middle East UAE, Saudi Arabia, Israel 5 – 20 business days
Rest of world Most supported countries and territories 5 – 25 business days

Note: Delivery times are estimates and not guaranteed. Exact rates are confirmed at checkout with Printful live shipping data. Shipping is unavailable for Russia, Belarus, Cuba, Iran, North Korea, and Syria.

Shipped worldwide · professionally printed and fulfilled

The mathematics

About this system

Turing patterns emerge from Alan Turing's 1952 reaction-diffusion mechanism: an initially uniform mixture of two chemicals spontaneously breaks symmetry into spots, stripes, or labyrinths simply because the chemicals diffuse at different rates. Turing proposed this as the explanation for the markings on animal coats — leopard spots, zebra stripes, fish patterns. Each image is the equilibrium state of a Turing simulation, the patterns self-organizing from random initial noise.

In the Turing Patterns collection

Turing patterns are the spatial structures that arise when two diffusing chemicals react at different rates. Alan Turing showed in 1952 that under the right conditions, an initially uniform mixture will spontaneously break symmetry and settle into stripes, spots, or labyrinths — purely as a consequence of diffusion rates and reaction kinetics, without any external template. The same mechanism is now believed to govern the markings on fish, the arrangement of hair follicles, and the branching of fingers in embryonic limbs. Each image in this collection is a Turing simulation run to equilibrium on a high-resolution grid. The patterns are not designed — they self-organize from random noise, the way they do on a leopard.

∂u/∂t = Du∇²u + f(u,v), ∂v/∂t = Dv∇²v + g(u,v)