Lines over time: Method 'A' treats the space of the paper as catalog of variables. Series 001 simply repeats the same line in columns beginning at the top left. The spacing is consistent. The lines are as close as possible before the bleeding ink renders them.

Two Overlapping Dash Size and Ratio Matricies: Method 'A' treats the space of the paper as catalog of variables. Series 005 is a spinoff of series 004, where the vertical dash to gap ratios are related to the vertical axis and the segment size is related to the horizontal axis. Series 005 overlays two such matrices. In this run the two sets are drawn with red and blue pens with varied densities. Furthermore, the red set's vertical and horizontal axes are scaled relative to those of the blue set.

Figuration: Method BB uses 2-D Bezier curves with two layers of hierarchy. Major curves are set with respect to compositional agendas. Minor curves are interpolated between major curves. Lines are drawn based on curve geometry at points along each curve. In set BB-001 each curve is divided evenly. At each division point rectangles are generated based on the position and local curvature. Each rectangle is assigned an incremented depth value as though it were recessed into the page slightly higher than the previous rectangle. Lower rectangles are occluded by earlier and higher rectangles. In run 004, the lines of the rectangle are drawn so as to not quite meet at the comers. Occluded lines are not drawn except for a momentary, contact point with the paper at each end point. A fresh black pen was used for both the lines and points. The large size–and duration–of this drawing leads to the pen's deterioration over its course.

Sphere with Dashed Lines

Rocky Sphere

Rolling: Method BC begins with a surface, which is then parsed, traced or divided to eventually inform marks on paper after undergoing some form of projection. Series BC-012 involves a parallel projection of the surface. Lines made up of straight segments are drawn vertically and horizontally within the space of the surface. Every other segment in each line is of a common length in three-dimensional space and is oriented normal to the surface. Intermediate segments connect the end of these segments to the start of the next segment, forming a continuous line across the surface. As the surface approaches flatness parallel to the "picture plane" (the paper) , the surface-normal segments approach zero length and the geometry of the line approaches that of a single straight segment. In run BC-012-001 horizontal lines are drawn with an aged but un-worn pen. Vertical are drawn with a fresh pen.

Little Ants Becoming Infinity: Method BE is inspired by Spirograph drawing toys, which are plastic devices in which a plastic gears are manually rotated within a plastic ring, which is also lined on its interior with gear teeth. Gears of various sizes and with pen holes at different locations yield a large set of possible geometries as they are deployed. In a digital environment, similar constraints are applied to create a drawing, but these constraints are variable, and geometry other than a traced point is used to create a drawing. In series BE-003, the “gear” grows in size as it progresses around the ring. A line through the center of the gear is drawn at each step. Alternating green and magenta pens are used in run BE-003-003.

Walking From Green to Blue: Method 'D' involves algorithms that treat the paper as space and ink as object. "Line" remains open to interpretation. In series D-002, marks are made by a particle "walking" in a random but generally curving path within a boundary on the page. The invisible particle leaves a dashed trail, which it is never allowed to make contact with. If the particle is nearing collision with its tail, its angular acceleration increases–it steers out of the way. The gaps between the dashes are openings, where the particle may move through. Over the course of the drawing, the particle speed decreases, (causing the curves to be tighter and smoother) the proportion of dash to gap decreases. Run 007 adds the variable of a second ink color to further emphasize the axis of time in the making of the drawing. Later marks have an increasing likelihood of being made with the blue, as opposed to green, pen. Also, run 007 uses a circular boundary frame and the start speed is slower relative to previous runs.

Densely Towards Spherical Figure: Method 'C' draws lines in sets with respect to a focal point. In Series 004, a single coarse path is calculated first, within a circular boundary. The path tends to avoid intersections. A finer path with 50 points is generated per each initial point, and forms an interpolated spine curve. Each new point marks the beginning of a drawn line towards, but not ending at, the focal point. Lines stop at any intersection with the path. Run 001 is the result of a 120-segment coarse curve. The plotter is loaded with a highly worn pen.

Walking From Red to Blue: Method 'D' involves algorithms that treat the paper as space and ink as object. "Line" remains open to interpretation. In series D-002, marks are made by a particle "walking" in a random but generally curving path within a boundary on the page. The invisible particle leaves a dashed trail, which it is never allowed to make contact with. If the particle is nearing collision with its tail, its angular acceleration increases–it steers out of the way. The gaps between the dashes are openings, where the particle may move through. Over the course of the drawing the particle speed decreases, (causing the curves to be tighter and smoother) the proportion of dash to gap decreases. Run 008 adds the variable of a second ink color to further emphasize the axis of time in the making of the drawing. Later marks have an increasing likelihood of being made with the blue, as opposed to red, pen. Also run 008 uses a circular boundary frame.

Stone Wall

Room C1 Blue Hatched: Method DB uses spherical projection to and a system of hatching to transform 3-D solid surfaces into lines. Each line on paper is informed by its position in (3-D) space and position on (2-D) paper. Hatches are computed first (Rhino Python) based on distance to camera and surface orientation, projected to a position on paper, occlusions resolved using a binary space partitioning tree algorithm (well-documented in Graphics Gems V) and finally lines are trimmed (Python with Shapely Library) and plotted (Python with Chiplotle Library). Series DB-001 represents a room inclosed by a 3-D array of rectilinear solids.

Cascading Lines Break the Circle: Method DC uses three kinds of base geometry: seed points establish epicenters of radiating lines; guide lines transform portions of lines that cross over them, effectively "pulling" them along their path; and trim lines leave gaps along their paths. At each step in the algorithm, one new shape is drawn at offset from its previous position. Intersecting shapes merge. Offsetting is irregular with slightly more spacing at the right than the left. This irregularity functions as a depth cue implying three-dimensional surface. Series 006 uses three points, and concentric circles as the trimmers and guides while the shapes are drawn as continuous lines at their boundaries. Each of those lines is assigned randomly to one of four groups. In run 020, the groups are drawn with four different pens, and one area of lines is allowed to grow beyond the prescribed circle.

Blue Radial Beta: Method IC involves using a digital simulation of a physical drawing apparatus. The digital simulation mixes forces and geometries that would be impossible to manifest in reality. A line is modeled between an anchored point on a path curve and a point in space, which is subject to gravity-like force. The modeled line exerts spring-like force onto the point in space, which is traced to produce a drawing. Various other artifacts exert forces on the point, which cause it to move, along with gravity and the spring force. Over the course of the drawing, the anchor point moves along the path curve. In series IC-004, the path curve is a straight densely coiling line that fills a circle. Points spread throughout the composition exert very weak repulsion forces on the drawing point. Run IC-004-002 is the results of two overlaid simulation layers, each with slightly adjusted spring forces. The anchor point moves along the path with enough speed to keep the drawn point lagging behind, despite the tendency for a pendulum effect. Near the center, the forces calm and the modeled line flips to the other side of the path. One layer is drawn with a fresh cyan pen. The second layer is drawn with a worn blue pen, which depletes over the course of the drawing.

A Little Fish Embryo: Method IC involves using a digital simulation of a physical drawing apparatus. The digital simulation mixes forces and geometries that would be impossible to manifest in reality. A line is modeled between an anchored point on a path curve and a point in space, which is subject to gravity-like force. The modeled line exerts spring-like force onto the point in space, which is traced to produce a drawing.

Storm with Explicitly Articulated Clouds: Method J consists of “whole world” simulations, but with accurate “real world” forces “incorrectly” applied. The space of the world is two-dimensional, and corresponds to the extents of the paper. These are not snapshots: the entire duration of each world’s existence is here in the drawings. Gravity exists as a universal downward force in these worlds, but the force is variable, not constant. Although the behavior of particles is labeled to correspond to phenomena in our world, scalar distinctions are short-circuited. Flaws are built in. Atoms are bound by mechanical springs, for example. Time is measured algorithmically in steps, and materially through the gradual deterioration of ink. Series J-009 adds the definition of "clouds," which are defined simply by a quantity of connected atoms and drawn with a bounding line.

Clouds Only: Method J consists of “whole world” simulations, but with accurate “real world” forces “incorrectly” applied. The space of the world is two-dimensional, and corresponds to the extents of the paper. These are not snapshots: the entire duration of each world’s existence is here in the drawings. Gravity exists as a universal downward force in these worlds, but the force is variable, not constant. Although the behavior of particles is labeled to correspond to phenomena in our world, scalar distinctions are short-circuited. Flaws are built in. Atoms are bound by springs, for example. Time is measured algorithmically in steps, and materially through the gradual deterioration of ink. Series J-010 omits the atoms from the drawing and renders only the lines of the "clouds," which are defined simply by a quantity of connected atoms and drawn with a bounding line.

Swarming Striations at time 90: Method 'K' uses an underlying set of points as the structure of each drawing. In series 002, the point positions are subject to swarming behavior. Sweeping laterally across the field groups the points according to their x position. Each group is then sorted according to their y position and a single line is drawn through the sorted points in each group. Every 1 in 50 lines is omitted. The points are initially organized on a grid; by run 90, the grid is a distant memory and points are so unevenly spaced that ridges and cliffs and other breaks in the apparent continuity of the striates surface register.