Lee Trent
I've been making digital art for over eleven years, starting with
bored attempts to draw geometric shapes in MS Paint in a middle school
computer lab, and escalating quickly. Through high school my work was
usually abstract symmetries and geometries of both space and color.
Since beginning university my work has typically blended mathematical,
scientific, and natural images. Even more recently the need to portray
mathematics precisely has necessitated coding to generate images, but
artistic details are often still added manually. The more math I learn
the more I want to be able to portray it, and the more art I make, the
more math I find myself wanting to learn to explain the patterns that
arise naturally in the process.
The koch curve can be generated by repeatedly replacing each
segment by four smaller segments, and the dragon curve can be
generated by repeatedly replacing each segment by two smaller
segments. In this piece, I used Processing to create hybrid curves
which use some of both segment replacement styles. All curves
began on the same initial segment, then followed one of the 8 ways
to choose either dragon- or koch-style replacement at each of
three steps, then they cycle through those three steps three more
times. Each curve has gone through 12 segment replacement steps.
The lines in the background connect curves whose three initial
replacement types differ in exactly one place.
The dragon curve can be generated by repeatedly replacing
individual line segments with two other line segments, which
create a 45:45:90 triangle with the original line segment. I used
Processing to generate "skew" dragon curves, where the segment
replacement instead creates x:(90-x):90 triangles, for x from 35
to 55 degrees, at 2 degree intervals. Similar patterns emerge as x
gets larger or smaller, but the overall curves for large and small
x are still rather different. These curves have gone through 20
segment replacement steps. The "canonical" dragon curve appears in
both the bottom left and top right.