Bridget Riley Arrest Riffs

Embryo geometry: a theory of evolution from a single cell to the complex vertebrate body

24 “blueprints” that illustrate how the musculoskeletal, cardiovascular, neurological, and reproductive systems evolve through the mechanical deformation of geometric patterns. These images show how the vertebrate body might have evolved from a single cell during the evolutionary time and during individual development.

Though neither rigorous nor exhaustive in an empirical sense, our model offers an intuitive and plausible description of the emergence of form via simple geometrical and mechanical forces and constraints. The model provides a template, or roadmap, for further investigation, subject to confirmation (or refutation) by interested researchers.

The concept of “embryo geometry” suggests that the vertebrate embryo might be produced by mechanical deformation of the blastula, a ball of cells formed when a fertilized egg splits. As these cells multiply, the volume and surface area of the ball expand, changing its shape. According to the hypothesis, the blastula preserves the geometry of the initial eight cells generated by the egg’s first three divisions, which establish the three axes of the vertebrate body.

Though speculative, the model addresses the poignant absence in the literature of any plausible account of the origin of vertebrate morphology. A robust solution to the problem of morphogenesis—currently an elusive goal—will only emerge from consideration of both top-down (e.g., the mechanical constraints and geometric properties considered here) and bottom-up (e.g., molecular and mechano-chemical) influences.

Origin of the vertebrate body plan via mechanically biased conservation of regular geometrical patterns in the structure of the blastula, David B. Edelman, Mark McMenamin, Peter Sheesley, Stuart Pivar

Published: September 2016, Progress in Biophysics and Molecular Biology DOI: 10.1016/j.pbiomolbio.2016.06.007

Two Dendritic Julia sets “Mating” to cover the sphere.

From the AMS-MAA Invited Address, What is the shape of a rational map? by Sarah Koch, University of Michigan. (Abstract) (paper 1) (paper 2)

Hear her discuss her talk and what it’s about here!

More about the Mating process and other videos of various types of Julia sets mating here!

Julia sets: numberphile

myalltimenews.blogspot.com

What Fraction Is Shaded? Challenge From The UK

What Fraction Is Shaded? Challenge From The UK This is a really fun geometry problem. It comes from the UKMT, a test which is part of f

Um probleminha divertido de geometria plana.

Sum of Triangular Numbers.

Happy winter break, friends.

Mathematics is beautiful. <3

Cool !

It’s a serious issue!

WAVES — Visualizing sound through cymatics and resonant frequencies | Phenomena - from ABC Science

Uncovering the geometric nature of soundwaves. This is visualized by directing sound waves through water and salt. The water rests in an upright facing speaker, and the salt rests on a high frequency mechanical wave driver. When the devices are activated with specific frequencies, the water and salt particles vibrate in synchronization with the soundwaves, forming incredible geometric patterns. Phenomena fuses art and science together to explore naturally occurring patterns, and the fundamental forces of nature that create them, to take us on an ambitious, innovative, and psychedelic journey through the fabric of the universe. Filmmaker Josef Gatti recreates nine ‘phenomena’ to produce mesmerizing art films, which are then paired with an original music score by Kim Moyes from Australian dance music duo The Presets. #PhenomenaTV