Water Power in Montana

October 26, 2008 - 10AM
Hydroelectric Generator
Bigfork, Montana

Some of us live off the grid. Most of us live on the grid. This town really lives ON the grid. Plenty of inexpensive electric power available here. Just bring your own copper cable.

Quiet Dedication to the Catch

24 October 2008; 7pm
Bigfork Montana
Fishing on the lower Swan River

"A River Runs Through It."

The last time I was here the river was a raging cauldron of white water, five-feet deeper, and filled with kayaks. The spring run off turns this river into class-five river challenge. If you are so inclined get out here in late May.

No, I'm not the fisherman in this picture. I'm taking the picture.

Wyoming landforms

23 October 2008
On Delta 737-800 body, Flight #1261 out of Boston to Salt Lake city @ 35,000 feet 8:57 am EST, somewhere over central Wyoming or eastern Utah.

Land spotting with Delta

Landform Geometry

23 October 2008
On Delta 737-800 body, Flight #1261 out of Boston to Salt Lake city @ 35,000 feet 8:30am EST, somewhere over eastern Wyoming.

A mix of geometric shapes. Early morning shadows highlight fractal plateaus, geologic curves, and the footprint of human farming and road building.

Wyoming from 35 thousand feet

23 October 2008
35,000 feet, somewhere over eastern Wyoming.

A mix of geometric shapes. Fractal landscape, geologic

Great Blue Heron

21 October 2008
Great Blue Heron, Hopkinton State Park, 7:45am, 135mm

The heron just stood there and let me get within 15-feet.

Go figure. It's early morning. Cold. I'm shivering and have to shoot this hand-held, gloves and all. Where's my tripod! All-in-all, not bad though.

Water and Rock

18 October 2008
Broadmoore Audubon Sanctuary, Natick Massachusetts:

Water and Rock. The interplay of two fluids. One, a material that is able to flow at a time scale that we can interact with. The other, a thicker material that flows at such a slow rate that it would take centuries of careful observation to be able to perceive its movement.

At this scale we can touch the movement of one and believe in the solidity of the other. But if we examined both of these substances at some atomic level we would not be able to determine a difference between them. Both would move at terrible speeds. Both would seem a cloud of motion and of indeterminate location.

Color and Texture

18 October 2008
Broadmoore Audubon Sanctuary, Natick Massachusetts:
Fractals in nature. Color. Texture. Shadow. Pattern. Space.


Nature is fractal at many levels. At a macro level this image emphasizes the overlapping shape and color of Lillypads on water. The space surrounding the Lillypads is broken up with the random distribution of grass and algae floating on the pond. If the identity of the plants over powers the broken geometry try examining the space between these objects to see an even richer fractal texture and geometry.

Voronoi Tessellations

The use of Voronoi diagrams can be traced back to 1644 and Rene Descartes. Voronoi diagrams were used by Lejeune Dirichlet in a 1850 study of quadratic forms. John Snow (British physician) illustrated in 1854 that the majority of people who died of cholera in the Soho area of London lived closer to a particularly infected well, located on Broad Street, than to any other water pump by using Voronoi analysis.

Voronoi diagrams are used in meterology and geophysics to analyze spatial distributions of rainfall and resources. They find contemporary use in city planning and marketing where a "best" route to a city hospital, or best location (relative to the nearest competition) of a store can be mathematically determined.

Named after Georgy Voronoi, a Voronoi tesselation is a plane of S points (Voronoi sites) where each point s is in a cell V(s) that consists of all points closer to s than to any other site. A Voronoi node is comprised of all the points that are equidistant to three (or more) sites.

// The Voronoi diagram shown is a set of random points in a plane //

In general, the set of all points closer to a point c of S than to any other point of S is the interior of a (in some cases unbounded) convex polytope called a Voronoi cell for c. The set of such polytopes is the Voronoi tessellation corresponding to the set S. When the dimension of the space is 2 the Voronoi tessellation can be easily drawn (as shown) and are sometimes referred to as Voronoi diagrams. When the space is 3 or higher the tesellations are complex and difficult to envison. Want to know more? Ask, or visit Wikipedia or Wolfram's MathWorld.