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Monday, June 02, 2014

Conservation laws and self-organization 

perturb
compensate
overshoot
compensate
overshoot more (feed-forward)
. . .
reach limit
compensate
overshoot less (feed-back)
compensate
balance

centrifugal/evolution
centripetal/involution

relationship to symmetry and conservation laws using 3D editing as a metaphor:

Shift 3D scene to allow 2D symmetry enhancement from a limited view

If the alignment is wrong then the local symmetry can destroy global symmetry

If the alignment is close enough then the problem can be overcome with a series of small local adjustments from different 2D views

2D Symmetry around a point involves summing to zero (conservation in one dimension)

2D symmetry around a line involves mapping pairs of point across an axis that sums to zero

The point or axis of symmetry provides a kind of compression function









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