This registered cortical template can be used to accurately predict the location and retinotopic organization of these early visual areas from cortical anatomy alone. This registration is then applied to the flattened cortical surface anatomy to create an anatomical template that is linked to the algebraic retinotopic model. We use a mass-spring-damper simulation to create a registration between functional MRI retinotopic mapping data of visual areas V1, V2, and V3 and an algebraic model of retinotopy. Here, we show that this limitation is overcome by correcting the geometric distortion induced by cortical flattening. Flattening of the curved surface to a plane unavoidably introduces local geometric distortions that are not accounted for in idealized models. A limit to the practical application of this structure-function model is that the cortex, while topologically a two-dimensional surface, is curved.
Within cortical visual areas V1, V2, and V3, algebraic transformations can relate position in the visual field to the retinotopic representation on the flattened cortical sheet. This entry was posted in Beautiful math, Math and tagged apollonian gasket, wolfram mathematica on by Luca M.Several domains of neuroscience offer map-like models that link location on the cortical surface to properties of sensory representation. The Circles of Descartes (Wolfram Demonstrations Project) – Contributed by: Ed Pegg Jr (you’ll need to have the Wolfram CDF Player installed to play with this full simulation).Apollonian_gasket A Tisket, a Tasket, an Apollonian Gasket (pdf), Dana Mackenzie, American Scientist, 2010.
To produce a full gasket the code should be longer than that allowed by a twitter length, but I think that a basic one could be done in about 500 characters or less. Well, actually that is not a complete Apollonian gasket, but it can give the idea. Here’s a very short code (under 128 character’s length) that I’ve made with Wolfram Mathematica guided by the saying “ Beautiful math can often also be very ]Īnd here’s the twit published by ( Wolfram (More info: ) #wolframlang /1aP7Wceob4
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