THESE ARE A FEW ANIMATIONS FOR THE PRESENTATIONS IN SECOND LIFE | |
| This is the result of the flow of a circle into a dipolar flow, with invagination along the midline
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| This is the animation of
the flow of a circle into a dipolar flow, with invagination along the midline.
The balstula is supposed to be circular, and to behave like a viscous material at long times. It is supposed to be incompressible, and thin.
The flow is supposed to act along a central furrow (the primitive streak), pulling forward the tissue towards the midline. There, the tissue disapepars underneath, this implies a free condition for the flow along the furrow. In this case, the flow is not conservative : the blastula loses matter underneath
(for extra-embryonic organs, eventually, and some other parts).
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This is the flow of a morula-blastula into a quadrupolar flow (it shows a set of regular lines forming
an internal structure of differentiation, as it is advected in the flow).
One understands that a structured ("textured") disc, will end in a textured "animal",
after being twisted, bent etc. in the flow. However, if fate maps are formed by cell differentiation (lineages) at the morula stage, completely different animals will be formed with different flows (say, a hyperbolic flow, and a centro-symmetric flow),
although they will all have homologous organs (say, gonads, stomach, etc.).
The idea is that a mosaic, which flows deterministically in a viscous flow, converges towards a complex shape, which has to be calculated by coupling the texture (cell lineages) and the flow.
There exist now very complex numerical simulations, simulating "everything".
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This is the animation of a morula flowing in a moving quadrupolar flow. The animation shows, supposedly,
the formation of
the shoulders and hips. The calculation shows that the effect can be obtained very simply with
a two parameters model : the position of the vortex cores away from the body axis
(roughly the width of the chord), and the position of
the hyperbolic point along the Antero-Posterior axis (the position of the navel).
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This is the result of a flow in an extension flow
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This is the animation of a blastula flowing in an extension flow.
The purpose of these animations is to show that with an analytical
expression (exact mathematics, see maths page) containing very few parameters (here only the length
of the pulling segments and the position of the hyperbolic point),
one gets a flavour of the animal
formation vey much reminiscent of what is observed, in terms of topology, and embryo "fluidity").
Notice especially that the brain and heart territories
form horse-shoe shapes, as well known.
The caudal (anal) opening closes completely.
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| Animations continue. See more images and animations
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Go to mathematical formulas Mathematics of vortex flows
Go to references
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