#Turing Patterns

MORPHOGENESIS III The synthesis of mathematics and biology. Inspired by the myriad patterns found in nature cellular structures, marine life, corals, plant growth, fungi, and animal markings as well as the textures sculpted by wind and water across the Earth’s surface. made with @touchdesigner - Music Agitate - Brendon Moeller #morphogenesis #generativeart #fractals #madewithtouchdesigner #touchdesigner #generativedesign #audiovisual #videoart #nature #pattern #motazari #mathematics #arts #artscience #newmediaart #turing #turingpattern

FISH TURING PATTERNS 🐠 Turing Patterns are interesting phenomena that occur in mathematics. Think back to every time you've seen the stripes on a fish, zebra, or the spots on a leopard? Its clear that pattern is not accidental, but exactly how is it doing this? Normally, flow would create streaks, but nothing is 'flowing' on the skin of these animals. Instead, it is thought this process is occurring completely naturally through diffusion! In chemistry class, you'll learn that reactions happen until there is no more reactants. When you consider these quantities occurring in space, it is a little more complicated! The equations that describe how these quantities are spreading throughout space, and also reacting with eachother, are given by "Reaction Diffusion" equations. Here, you see one model of a reaction diffusion equation, the Gray-Scott model, with the standard Laplacian, replaced with the Laplace-deRham operator, to be able to be switched to the surface of a fish. In this equation, for the right parameters f, k, Du, and Dv, the spotted pattern appears on these fish. #algebra #differentialgeometry #surface #tensor #calculusofmothernature #exteriorcalculus #calculusofmovingsurfaces #science #biology #biophysics #bioengineering #engineering #signals #fluidmechanics #condensedmatterphysics #graphicdesign #computergraphics #waves #grid #quantum #quantummechanics #physics #discreteexteriorcalculus #nature Music (🎶): Outrun ( @mornetwork) - Rituals

James Turrell on Acid 🤪 Learned some new tricks for a project and heres an exploration from it 😎 I think I’m in my blurry era and I hope you are on board 😘 - #jamesturrell #acid #trip #tripping #pattern #motion #animation #zzmotion #zzdesign #zipengzhu #gradient #color #motiongraphics

Curlicue Fractals #fractals #satisfying #geometry #pattern #asmr #adhd #ocd #math #spirograph

These are Turing Patterns. A balance of reaction and diffusion. Developed by who is considered by some to be the inventor of the computer, Alan Turing. These patterns are simulated with a computer algorithm that uses differential equations. Mathematics is spiritual practice. A formal endeavor to elucidate the mind and awaken love. Love is all that matters. Happy New Year. 2024. #Love #Meditation #Mathematics #Enlightenment #TuringPatterns #ReactionDiffusion #ComputerScience

By @thebhaktimathguru: ∂u/∂t = Du ∇²u + f(u, v) ∂v/∂t = Dv ∇²v + g(u, v) Turing Patterns by the Gray-Scott Model. ∂u/∂t = Du ∇²u - uv² + F(1 - u) ∂v/∂t = Dv ∇²v + uv² - (F + k)v

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2 Point Torus #sacredgeometry #art #circles #lines #torus #illusion #animation #welcometothegoldenpage

The Fingerprints of Nature 🌿 🕵️‍♂️ [Watch till end] . These are known as Turing patterns, created through a fascinating process known as Reaction and Diffusion. Diffusion is simply substances moving from an area where they are more concentrated to one where they are less concentrated. Reaction is when two substances interact to change into other substances, or to create or remove one of the substances involved. These captivating patterns emerge by tweaking specific values in the reaction-diffusion equations. This simulation uses the Grey-Scott Model, a famous approach for generating Turing patterns. These patterns are visible in nature, from zebra stripes to seashell designs, helping species survive by camouflaging or attracting mates. In everyday life, they guide the design of materials for aerospace and optimize urban layouts to reduce congestion. Far from just theoretical, these patterns influence real-world applications and future innovations. . Created using Python 🐍 . . . #maths #mathematics #code #python #weekend #nature #union #visualize #physics #chemistry #biology #science #reaction #diffusion #simulation #universe #project #equation #pattern #symmetry #asmr

Does this remind you of something? Toroidal symmetry drawn by a spirograph. 2D Hypotrocoid /Orthogonal Toroidal Symmetry seen from the top view of a Torus designed by Epicycles through the spirograph. The spirograph is a device of geometric design that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrocoids, curves directly related to toroidal geometric motion. From microcosm to macrocosm, spiral and polygonal shapes are seen throughout nature and obey the same geometric and mathematical laws as Cyclic Vibrations, being the basis of morphogenesis or the formation of life and matter. ⚝ Tag your friends who will remember the Spirograph so they can re-signify what the patterns of this simple "toy" really imply. Video by Morgan Manke

Did you know that no two cows look the same? The same mathematics that governs your fingerprints also produces the patterns on cows and many other animals. Discovered by Alan Turing, they’re called Turing Patterns. Written and produced by @arckopolo Hosted by @casper_mebius #veritasium #science #physics #turing #cows

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