Tiling, Bravais Lattice, Squiggles

This is the first successful image in a new project that grew out of my tilings project. I created the image in three steps. First, I made a non-periodic tiling. Then I generated a lattice of vertices including all potential vertices around each tile. Then I plotted a shape or lines (in this case, a squiggle) at each lattice point. The plot of vertices is somewhat like a Brazais lattice, though I'm extending this math concept for my own purposes.

Tilings of the plane using tile sets of regular polygons, rectangles, isosceles triangles, trapezoids, and parallelograms, have vertices that lie in characteristic patterns or lattices depending on the properties of the polygons — its angles and sides. The Bravias lattice system categorizes these patterns. The five Bravais lattices for two dimensions approximate the arrangement of vertices of simple periodic tilings. I'm applying this concept to complex, non-periodic tilings with large tile sets.

Storm, Sepia Approach (Hexamerism Lost)

This is titled "Storm, Sepia Approach". The tile set could have made a hexameric tiling starting with the center hexagon. I forced the off-balance tri-radial asymmetry.

Gratuitous link: I suggest you look at the paintings of Janice Biala.

Pentamerism

This is the only non-periodic tiling I've done that is pentaradial. It has five polygons, but the square and rectangle (which has an aspect ratio of 1:1.618033989) can only be used along the five rows extending from the center pentagon. If I attempt to use them anywhere else, a gap is created.

Camouflage

In 2007, the Portland Art Museum exhibited Camouflage, an exhibition of eight paintings that explored artists’ use of pattern. The exhibit included a large camouflage pattern painting from a series that Andy Warhol did around 1986.

In his 1940 essay, A Mathematician's Apology, G. H. Hardy (full text here) discusses, among other things, pure versus applied mathematics with one difference being the application of mathematics to war. He stated that "a mathematician was a maker of patterns of ideas, and that beauty and seriousness were the criteria by which his patterns should be judged".

In Arthur Danto's The Transfiguration of the Commonplace: A Philosophy of Art, and 25 years later in his 2008 reply to his critics in CA online, Danto uses Warhol's Brillo box to discuss what makes an object an art work. (See Ontology, Criticism, and the Riddle of Art Versus Non-Art in The Transfiguration of the Commonplace. Contemporary Aesthetics, Volume 6, 2008.)

The Warhol camouflage series is interesting in that it turns a pattern designed for war back into art. Hardy said "A painting may embody [an] 'idea', but the idea is usually commonplace and unimportant." I wonder what he would have thought about the Warhol painting's ability to wrap all these concepts — beauty, seriousness, the ontology of art — in one art work.

Here's an unrelated, gratuitous Bezier curve image from a series:

Here are a few close-up pictures of a painting (a polyptych) just under way. It will resemble the digital print, Slip, but will undoubtedly have a completely different color scheme. I shot these as close as I could to show what I look at all day while I'm laying down these outlines in white on white oil paint. All the curves are paint applied with a small brush along pencil lines. The pencil lines are plotted/interpolated Bezier curves. That is, I plot about ten points per curve, and interpolate with ships curves or other French curves. The plots follow a spreadsheet of grid points that I exported from the original digital print program data.

Erosion

First test drawing of new program about erosion and alluvial fans:

Beziér Curve Drawing

The developer-artist has the ability to collaborate with a client, and enhance understanding of the project in the process. The client can propose a requirements list or request permutations based on variables built into a program. Architects, engineers, and designers work with developers to extend or modify software, achieving through collaboration a client-directed variation. The artist-developer creates a program which reveals more through the interjection of client requirements than an artwork rendered from just the artist's requirements.

This new "Beziér Curve" drawing was created with a Flash Air program written for managing and creating modules and whole drawings within this project. It's meant to explicitly demonstrate modularity open to client requirements. The client can dictate requirements for the arrangement of squares, the selection of curves within, the color and thickness of line, overall scale, or as yet to be determined requirements.