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Lorenz Attractor, Warm Eco Canvas

Lorenz Attractor, Warm Eco Canvas

Regular price $36.00 USD
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Simple equations have simple solutions. The assertion sounds reasonable, but over the 20th century mathematicians discovered how profoundly complicated dynamical systems can be merely by involving quadratic terms. Let \((x, y, z)\) denote spatial position, and let \(t\) represent time. In the 1960s, meteorologist Edward Lorenz and computer scientists Ellen Fetter and Margaret Hamilton studied a particularly simple-looking system of differential equations as a model of atmospheric convection: \begin{align*} \frac{dx}{dt} &= -10x + 10y, \\ \frac{dy}{dt} &= 28x - y - xz, \\ \frac{dz}{dt} &= xy - \tfrac{8}{3}z. \end{align*} An individual solution, rather than settling down to a point or loop as one might expect, instead moved unpredictably. Further, the qualitative behavior of solutions changed chaotically when the initial conditions were slightly varied. The image depicts randomly-chosen numerical solutions to the system. The two-lobed "strange attractor" that solutions "tend toward" can be glimpsed in the two eye-like loops near the center.

Made entirely from recycled plastic bottles and stretched over a lightweight, recycled frame, our custom eco canvases are a great way to introduce some sustainable art to your online store – even the packaging is made from 100% recycled content! Better yet, they’re almost half the weight of traditional wooden canvases and cheaper, too.

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