voronoi diagrams are how you divide space when you know where everything is
school districts or cell tower coverage
the kind of problem you solve with coordinates, a global view, and a computer.
a CSHL group just showed the chinese money plant solves it in its leaves.
each leaf has tiny pores called hydathodes around each pore, a closed loop of veins
when you map them, they are textbook voronoi cells with the hydathodes as the seed points. perfect geometry.
but a leaf cell has no coordinates. no ruler or map of the other hydathodes. it can only sense its immediate neighbors.
the trick: each cell follows one stupid local rule about pushing auxin to its neighbor. no global plan at ALL
just chemistry flowing forward in time
where flux from two pores meets at equal magnitude, a vein forms. that ridge IS the voronoi boundary.
the geometry isn’t programmed it’s just the steady state of a PDE running on a sheet of cells
the mature leaf is the answer to a computation that already finished.
there is zero information in the static leaf about how the auxin flowed, what the transients looked like, which cell did what when.
you could stare at a million leaves trying to infer “the rule.” you would be wrong. there is no rule
there is only the trajectory.
every static image of a living system is the screenshot of a computation nobody filmed.
we keep photographing the answer and wondering why we can’t reverse-engineer the math.
remind you of something?
@prof_g
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