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Reference
- which is more intellectual than visual.

Tutorial Material
- which is as much visual as intellectual

INFINITY in its Proper Place
(Perhaps best to start here!)

Path Curves & Real Buds; the Practical Mathematics

Drawn in his Notebook 44 years ago

sycamore

See
Path Curves Fitted to the bud below

pc_to_bud

There is a collection of Lawrence's own geometric drawings on Mr Ben Geels' excellent site—

http://www.edwardsgeometry.nl

Apologia

      Graham Calderwood

My mugshot

       book    Musings

THE BUD WORKSHOP

Research on Real Buds and Planets

Romanian Walnut 2006-2007

Romanian Walnut 2007-2008

A Bud is a Composite Thing

The Phase Shift

Models of the Phase Shift

Do Buds Change their Lengths at 14 Day Intervals?

Development of a 2-D Path Curve

pcDevframe
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For topical background
See
"path curves" on Nick Thomas' excellent site concerning Projective Geometry.
For a superb collection of mathematical information, visit  Eric Weisstein's MathWorld.
On that site, see especially General Projective Geometry, Projective Geometric Axioms, Desargue's Theorem, and Fourier.
See also, Anatomy of a Bud, by Jay Kappraff.
Finally, see Wilson's Conic Pages.

Lawrence Edwards' observations spanned decades, and he gave account of them in his book,  The Vortex of Life, pub. Floris Books

book imageResults of research conducted after this book was originally published are contained in seven volumes of the Supplement and Sequel to the Vortex of Life. These volumes are no longer in print , but they may be downloaded, in PDF form, here.

This site may one day become fully interactive.
Until that happens, you are invited to subscribe to
the Vortex of Life Conference mailing list.

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The Proceedings of the Vortex of Life Conference can be found at

http://vortexoflife.org.uk

Lawrence Edwards

This site is accumulating details of research on buds and planets.

The projective transformation of space into itself gives rise to path curves, than which no more elementary or simple curves exist.


Please enable Java for an interactive construction (with Cinderella).

It was one of Lawrence Edwards' many discoveries that path curves very accurately describe the form of the buds of a comprehensive range of species.

Click here to try it yourself on some real buds.

Edwards' research is the first and only one to have, from first mathematical principles, successfully described any biological form.
All other attempts at precision are essentially—and merely—statistical (norms are not principles). This implies that DNA cannot alone be the propagator of living form, and random process cannot alone drive evolution. How these things may work together is an obvious target for new research.
He discovered that buds change form rhythmically,

and that the rhythms are those of the alignments of the Moon with Bodies of the Solar System.

He found that a specific tree or flower changes the form of its buds in the rhythm of the Lunar alignment with a specific body. The Oak, for example, appears to change with Mars, the Beech with Saturn and the Birch with Venus.

Lambda_dips

One of his λ* charts is reproduced here (for a Beech bud near his home in Strontian, Scotland) that clearly shows the form of a real bud undergoing about fortnightly change - that is, in the rhythm of alignment (opposition or conjunction) of the Moon with a body of the Solar System—in this case, Saturn.

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Illustrating Alignment of Earth, Moon and Mars, and the corresponding change of bud form (none of it in the least to scale!)

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* λ is the " Shape Parameter", controlling the "sharpness" of the bud's apex relative to the "bluntness" of the bud's base.