The first part of this page consists of new renditions of graphics done
between 1972 and 1980 at Lewis & Clark College on pen plotters and TEKscope CRT's.
The GIF images were generated by linking into the
gifdraw library by Quest Protein Database Center, Cold Spring Harbor Labs.
(Actually, I called the routines from my own set of routines which can produce
PostScript, Tek4010, or GIF output). 2014 update: Really, I should generate SVG! That's next.
At the end of this page, I give some references to tree-related topics.
Trees
I am interested in tree structures of all kinds,
from simple geometric abstractions, to the fate map of cells during
embryogenesis.
Filling space by Hand
Here is 'Pixel Tree', drawn using MacPaint in the late 1980's!
Pixel Tree
Trees and the perfect reduction factor
Nice little N-ary Tree
The number given is the angle between branches.
I have been able to compute the perfect reduction factor to use in each case.
In Fall of 1979, we recorded 1300+ trees frame-by-frame on Super8mm film.
This was a fun Independent Study project done with student David C. King.
See YouTube for the one of the original films
Geom-e-Tree (1980)
and a digital replica using Processing
Geom-e-Tree (2012).
Radial Trees
These trees are drawn on concentric circles using two different
radius functions. I.E., a reduction factor (Rf) is NOT applied to the
length of the branches, but there is a recurrence relation between successive radii.
Recurrence Relation Method #1 assures that the areas of the concentric shells are the same.
Input R from keyboard;
R = R * (1 + pi/n);
Binary Radial RR#1
Recurrence Relation Method #2 is left as an exercise the reader. LOL
Input R from keyboard;
A = R^2;
R = SQRT( A + R^2 );
Binary Radial RR#2
There are others of higher degree.
These are very similar in shape to Dendrimers, or molecular trees.
See below.
Nested Polygon Sequences
Not Tree-related, but included here when I first made this web page in 1990's.
Done for John K. Richards in 1973, using a CalComp plotter.
Will write story behind it some day.
Visual Arts (VA) copyright registered in April 1978 under title Synergy.
I made a series of plots varying 3 paraemters:
Notation n[i|o][+|-]c)
n is the number of sides for initial polygon
i|o is the direction (inward or outward)
+|- is whether to increment n or decrement n
c is the integral change for 'n'
Note that while the figure is named 3o+1, it was drawn as 30i-1...
I started with a 30-gon of a given radius, and went inward (inscribed) from there.
Dendrimer Molecules
See May 1995 Scientific American. This article describes the
contruction of tree-like polymers. It has a diagram similar to the radial
trees above. The possibility of such molecules had occurred to me as well
when I was drawing all these trees.
See also February 23, 1996 Science: Self-Assembling
Dendrimers, p 1095; Molecular Trees: A New Branch of Chemistry, p 1077.
Both articles contain bibliographies.
See October 1994 Scientific American, Page 112. Hans P.
Moravec at CMU designed a binary tree-shaped robot - trunk, two arms with
two limbs each, etc, down to many tiny fingers.
Polygonal Billiards
early polygon flux
Paths of particle reflections (bouncing around) inside regular
concave polygons. Originally conceived in 3D to explore internal reflection
dynamics of pyramid structures. When that proved difficult, I dropped to 2D
to see if any interesting things happen. First program for Triangles by
Corey Hirsh. Generalized polygon program by myself. Debugged by Greg Davis!
I recently discovered that others have done math research on this exact subject.
Sorry for the bright colors.
The number given is the angle of the initial ray, beginning at the center
of the polygon.
In 2011 I wrote PolygonFlux, an immersive iOS app, that allows one to explore this space, and later, PolygonJazz, combining sound with geometric flux.
For a complete history of all this, see
[LINK].
