How the "130 Generic Causes of Form" May In Fact Cause Or Influence Physical Or Pure Shapes

(Or Their Nature, Genesis, Growth, Evolution, Engineering Construction, Degeneration, Transformation, Manipulation, Behavior, Interaction, Conceptualization, Uses, Processes, Mathematical Definition Or Assemblage, Diversity, Specialization, Laws, Interrelationships, Properties, Analogs, Homologs, Phenomena, Incidence, Distribution, Maintenance, Stability, Etc)

ANASTOMOSIS

  • Ex. 1: When it reaches a level floodplain, anastomoses can transform what had been a DENDRITIC or UNILINEAL river into a NETWORK, in which the river's tributaries are also its distributaries;
  • Ex. 2: Just as the discovery of horizontal gene flow may force biologists to repicture the evolutionary TREE of Life as really an anastomotic NETWORK.
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    ANGLES:

  • Ex. 1: Angular changes can turn a CONVEX POLYHEDRON into a CUP-LIKE CONCAVE POLYHEDRON.
  • Ex. 2: Leaf litter on a forest floor has been turned into a matrix of diverse CURVED IRREGULAR POYHEDRA by the falling together of leaves at all sorts of angles and in compressive twists.
  • Ex. 3: ANGLES make a CYLINDER into a CONE.
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    ANISOTROPY

  • Ex. 1: The [shape, diversity, and habits] of [crystals and minerals] is in large part due to the manifold roles of anisotropy in their morphogenesis.
  • Ex. 2: When a shaped balloon inflates into its intended form, it does so partly as a result of predesigned anisotropies in its rubber.
  • Ex. 3: Soap BUBBLES - and FOAMS thereof - are MINIMAL SURFACES caused by the anisotropies of surface tension and polar molecules;
  • Ex. 4: The cells and intracellular membranes of organisms are kindred morphological manifestations of various and sundry chemical and biophysical anisotropies.
  • Ex. 5: Anisotropic morphogenesis could underlie ontogenesis - and might even be used to explain the evolution of all life.
  • Ex. 6: A humbler example is the CYLINDRIC elongation of a plant stem - whether via SOLENOID or meristem.
  • Ex. 7: Not only roots and worms but entire ecosystems advance along, and are shaped by, anisotropic gradients.
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    ANTISYZYGIES (meetings of opposites)

  • Ex. 1: Opposite surfaces can be joined or united - e.g. the top and bottom of a MOBIUS BAND;
  • Ex. 2: And even exterior and interior [surfaces and regions], as in the KLEIN BOTTLE.
  • Ex. 3: If the opposite ends of a LINE are joined one has a CIRCLE (which, incidentally, is by definition both finite and infinite).
  • Ex. 4: Two oppositely flowing currents may meet and form [SPIRALS, HELIXES, EGAGROPILES, KNOTS, CIRCLES, CONES, CATENOIDS, BUNDLES, LINE-CLUMPS, TREES, LATTICES, MEANDERS, WAVES, e/vc], thanks to eddies, turbulence, etc.
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    ATTRACTION

  • Ex. 1: All matter attracts and is attracted to all other matter, because of the universality and laws of gravitational force. On the cosmic scale this has as a consequence a progressive tendency for all free matter to become associated with other particles and parcels of matter and to aggregate in ever fewer assemblages of ever larger scale, or perhaps of ever greater hierarchical (and perhaps behavioral) complexity. Where gravitational attraction is dominant over other kinds of forces of [repellent, disintegrative, or purely stabilizing or resistive] character, or exceeds thresholds for the general [plasticity, free movement or net migration, compression, rearrangement, exponential growth or collapse, or transformation] of matter, self-attracting bodies tend to become uniform monocentric isotropic - perfect - SPHERES. In short, such attraction causes the universe to grow spheres - witness planets, stars, black holes, stellar nebulae, elliptical galaxies, atoms, perhaps even a hyperspherical cosmos.
  • Ex. 2: If one places iron filings onto a plate of glass with a magnet beneath it, magnetic attraction causes the filings to CLUMP, CHAIN, and align themselves in a SERIES OF ARCS along lines of force about and between the magnet's poles. Here in this single example one observes attraction simultaneously causing many different types of form: BLOBS, CLUSTERS, LINES, ARCS (CURVES), BUNDLES, WAVES, STRIAE or ARRAYS, RADIATIONS, CONES, etc. Indeed, a tendency to exhaustively evolve all genera and species of shape may be at work. Such a protean or omnificent principle might even be an intrinsic feature or latent potentiality of attractional morphogenesis in general.
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    BENDING

  • Ex. 1: A STRAIGHT LINE can be bent into a [CURVE, SINUSOID, or MEANDER - even a KNOT]: {{INSERT MINI-ILLUSTRATION}}
  • Ex. 2: Similarly, a FLAT [PLANE, POLYGON, or DISC] can be 'bent' into countless types of CURVED SURFACES, incl. [minimal-but-tendential (qualitative), asymptotic-but-open, or closed] [CYLINDERS, ROLLS (SCROLLS), CONES, and SPHERES].
  • Ex. 3: Many odd shapes - incl. ones that have been neglected by theory, art, technology, biology, or all of nature - can be produced by twisting familiar forms in simple or complex ways: one can create a self-swallowing SPIRAL by bending a hollow TUBE into its own mouth; a convex (or concave) CUBOID, by bending a CUBE'S walls outward (or inward); or a KNOTTED TREE, by bending a tree as a whole.
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    BRANCHING

  • Ex. 1: A CYLINDER can branch into a TREE, but so can a SPHERE or DISC (as in a BLOB), or a BUNDLE (as in a banyan tree, neural lemniscus, or folding umbrella), or a SPIRAL (as in a hurricane).
  • Ex. 2: The human body is branched laterally into two [symmetric and asymmetric] halves.
  • Ex. 3: An electric charge or current leaks away into a TREE WITH FRACTAL BRANCHES.
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    COLLINEAR ALIGNMENTS

  • Ex. 1: Collinear alignments of the points of a CLUSTER can cause the formation of a [CHAIN, LINE, LATTICE, NETWORK, EGAGROPILE, SPIRAL, BUNDLE, or even TRIANGLE (as in a flock of geese) or HIERARCHY (as in a harmonic spectrum)].
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