Tesselcat A tesselation pattern pierced into a turned catenoid form Sold

Tesselcat Walnut, Lacquer 10.5"H x 7.5"D

Tesselcat Detail of the tesselation

Ribbon Sphere Hints of a cube shaped ribbon contained in a sphere Available

Ribbon Sphere Ribbon- Massur birch and tung oil, Stand- Maple and Acrylics

Ribbon Sphere 6" D on sphere, 13" total height

Binary Black Hole A modified Lawson minimal surface Available

Binary Black Hole Form- Cherry, India Ink and Acrylics, Stand- Maple and acrylics

Binary Black Hole 13” x 9” x 2”

Euclid's Phenix A piece selected for the AAW’s “Rising” show. Sold

A sphere with flares arranged in an icosahedron standing on a complex mobius strip.

Euclid's Phenix Overall- 17.5” H x 7.5” D, sphere- 5.5” D

Riptide A collaboration with Ed Kelle. I turned the form, and he did the fantastic carving. Available

Riptide Maple
8” D x 7” H

Conic Inversion A minimal surface that joins 2 opposite cones with a surrounding circular border Available

Form- Ash, 7”W x 5”H, Bleach, Acrylics, Krylon.
Stand- Compwood, 12” Deep 11”H, Ink, Krylon

Oak Trefoil A collaboration with Andy DiPietro. Sold

refoil form; Chestnut Oak, Andy’s Oakobolo finish, 6” H x 7.5”D. Stand; Maple, dye, 7.125”H x 4”D. 13”H x 7.5” D together

Crossing Tunnels A minimal surface based on the Chen-Gackstatter form

Crossing Tunnels palted Tasmanian Rose Myrtle Burl, 5” x 5” x 6.5”, Bush Oil, Base is maple with leather dye.

Trefoil Waves Another collaboration with Andy DiPietro Sold

Form- Figured Ash, dyed blue on black finish, 6” H x 7.5”D. Stand; Maple, dye, 7.125”H x 4”D, 13”H x 7.5” D together.

Distortion II A minimal surface of the intersection of an Enneper form with a flat plane. Sold

Distortion II Maple burl, lacquer, 9” x 12” x 4”, 11” high on stand. Maple Stand, Feibings dye, lacquer.

Inversion A minimal surface that joins a trefoil knot with a circle as the outer edge. Sold

Figured big leaf maple, Bleach, stain, pyrography, 9" x 2.5”, stand is maple with dye and Krylon

Trefoil This is the first “Trefoil” piece I did and the one I like the best. Based on the Enneper minimal surface form with 3 lobes (hence the title). Sold

Trefoil Masur Birch, lacquer, 7”D x 5”H. Stand is maple dyed with Feibings and lacquer.

Trefoil Another view

Enneper A minimal surface based on the form that the mathematician Enneper described Sold

Enneperbr>Redwood burl, 3” x 4”, Bubinga stand.

Distortion The first of these pieces I did based on the intersection of an Enneper minimal surface with a plane. Sold

Distortion Maple burl, 10" x 8" x 3.5”, Oil. Bubinga stand.

4 Hungry Chicks Based on the Shoen hybrid triply periodic minimal surface. Available

4 Hungry Chicks Black Ash burl, 4.125" x 4.125" x 3.75”, tung oil/varnish mix

Tao of Geometry II

Sold

Form- Elder Burl, Aniline dye, bleach, acrylics, Bush oil 8”D x 3”deep
Stand is maple comp wood, ebonized with india ink 14”W x 4”H
Slate base

Costa Hoffman Meeks A minimal surface named for the mathematicians that described it with math. Sold

Costa Hoffman Meeks A very intriguing form. There are only 2 sides to the form shown by the different colors as a result of the tunnels that join the surfaces.

Costa Hoffman Meeks Bubinga, bleached on one side, lacquer. 9”D x 6”H. Branded and ebonized maple base.

Geometree
A piece turned from wood sent by John Jordan for Vicki Jordan’s “Beloved Tree” project. The form is a catenoid, and is meant to evoke the base of a tree. Jordan maple, 5”D x 7.5”H, pyrography, lacquer, acrylic (tire) and string.

Infinite Loop A trefoil knot minimal surface. The edges of the piece trace out a trefoil knot, and the wood joins those edges in a minimal surface. Available

Infinite Loop Elder burl, colored epoxy, oil. 5.5”D x 2”

Lawson A minimal surface described by the mathematician, Lawson, and inspired by vesicle-like microorganisms. Available

Lawson Ebonized Butternut, 8.5” x 5”

The Tao of Geometry Based on Infinite loop trefoil, with the middle twist removed. I did this with the intention echoing the Yin Yang Taoist symbol. Sold

The Tao of Geometry Black ash burl, 12"H x 3"deep x 8" diameter. Stained on one side, bleached on the other, Lacquer

Space Warp A minimal surface based on the intersection of a double Enneper minimal surface with a flat plane. Sold

Space Warp Corrugata Burl, Tung oil/varnish mix, 13” x 9.5 x 4”, acrylic stand.

Vortex A simple minimal surface, a catenoid. Sold

Vortex Red Maple, acrylics, 9”x9”.

Ancient Math Based on 3 interlinked rings known as Borromean Rings. A minimal surface joins the rings. Sold

Ancient Kauri. This wood is salvaged from bogs in New Zealand and is as old as 50,000 years. 5” x 5" x 5”, pyrography, lacquer

Ancient Math Another view

Open Wide A minimal surface that joins an outer circle with an inner ellipse at right angles to the circle. Available

Open Wide Maple from Vicki Jordan’s “Beloved Tree” project, lacquer, 5” x 3”.

Schwarz’s Cat A minimal surface that joins 6 circles centered on the faces of a cube with a catenoid base. Walnut, Tung oil/varnish mix, 6.25"h x 4.5"d Available

Parastichy A catenoid minimal surface (one of the simplest) pierced with 2 opposing spirals, 21 in one direction and 34 in the other. These are numbers that are part of the Fibonacci series. Available

Parastichy Box elder, acrylics, Fixatiff, 7” D x 8.5” H

Minimal Surfaces

I have recently been exploring the intersection of math and sculpture. One of the really cool things that I have discovered is the class of math objects called minimal surfaces. These are surfaces that describe the least amount of surface area that will connect a circumscribed area.

Soap bubbles will form a surface with the least amount of surface area with a given boundary. Bubbles have no boundary, so form the least amount of surface area for a given volume, a sphere. A loop of wire will result in a flat disc, bend the loop and the bubble will join the area in a smooth curve that minimizes the amount of film. More complicated structures can be made by creating bubbles from two or more loops of wire with a film joining the two (called a catenoid).

Mathematicians have been able to describe these forms using some complicated math that I don’t profess to understand. Luckily the results of their work can be plugged into programs that will show the result as 3D objects that can be manipulated by changing the variables. The mathematicians have come up with some very complex, and fascinating, forms which probably would not have been otherwise discovered. This is my attempt to translate their work into turned art.