My very first computer art piece. Both figures were initially drawn by hand, transferred to graph paper then converted to a lists of coordinate pairs. Care was taken to make sure each figure had the same number of points and lifted the pen in the same location. I used a simple math concept called linear interpolation to make the transformation between the two figures. I carefully choose the in-between fractions and hard coded to the code, not random.

This drawing uses the Goose figure from a set of hand-digitized representational images. The full set consists of: Goose, Frog, Fat Cat and Elephant. I often used these interchangeable figures in my early works. Digitized representational image of a the Goose placed at intervals along a space curve. Curves generated by a mathematical function written by Christopher Scussel. The Goose’s scale and orientation is based on data from the curve. The slope of the curve at a given point determines the direction of the bird figure. This is an early example of Generative Art. Many curves were drawn before this particular curves’ data set was determined. In essence, random to a point of being chosen by the artist.

Boxes I is a generative art "derivative" piece inspired by one of the earliest pioneers of the generative art medium: George Nees. In the beginning when we only had plotters to draw lines with the small community of computer artists produced works that inspired each other. His work called “Gravel” inspired me to create Boxes I and Boxes II. A regular grid of square tiles. As the computer draws each square its position relative to the center of the grid is calculated using the distance formula. In the case of Boxes I the closer the square is to the center of the grid, the more random displacement (translation) and rotation is allowed.

Boxes II is a generative art "derivative" piece inspired by one of the earliest pioneers of the generative art medium: George Nees. In the beginning when we only had plotters to draw lines with the small community of computer artists produced works that inspired each other. His work called “Gravel” inspired me to create Boxes I and Boxes II. A regular grid of square tiles. As the computer draws each square its position relative to the center of the grid is calculated using the distance formula. In the case of Boxes II the further the square is from the center of the grid, the more random displacement (translation) and rotation is allowed.

An Op Art inspired work. Bulges and Dents is a two tile tessellation where each tile is a tessellation. In one tessellated tile a mathematical function manipulates the drawing coordinates of a regular grid of tiles to appear to be pushed in (dents) while the other manipulates the drawing coordinates of a regular grid of tiles to appear to be pushed out (bulges). The mathematical function to do this was written by Christopher Scussel.

This drawing uses the Goose figure from a set of hand-digitized representational images. The full set consists of: Goose, Frog, Fat Cat and Elephant. I often used these interchangeable figures in my early works. Coming and Going is the juxtaposition of two spiral configurations. The digitized figure of a goose is drawn at function-based intervals tangent to each curve at the interval. Also, as the figures are drawn along each curve they are scaled up in the middle and down at the ends. Where the curves overlap, as one curves ends, the figures are rotated so they continue their flight path out into the second curve. Hence they come in on one curve and go out on the other. This notion is amplified by the fact that the figures are at there smallest size at the ends of the curves. This piece was inspired by the works of M.C. Escher.

The is regular grid tessellation made up of 9 column x 7 rows of tiles. Each tile is an interpolation between a smaller inner square and the larger outer square that contains it. The number of in-betweens in this variation is fixed and the position of the small, contained square is allowed to vary. It is translated within the larger square both horizontally and vertically by an algorithm the based on the sine trigonometric function.

The is regular grid tessellation made up of 9 column x 7 rows of tiles. Each tile is an interpolation between a smaller inner square and the larger outer square that contains it. The number of in-betweens in this variation is random. The position the small, contained square is allowed to vary (translate) horizontally and vertically by controlled randomness.

This drawing uses all the figures from a set of hand-digitized representational images. The full set consists of: Goose, Frog, Fat Cat and Elephant. I often used these interchangeable figures in my early works. I used to be an Engineering graphics professor. Back in the day, before CAD, we were developing algorithms for perspective drawing. In this piece I wrote an algorithm to randomly distribute my digital menagerie on the surface of a cylinder. Then I used the computer to draw the data using perspective drawing equations we had developed. The result is a one-point perspective as if looking through the length of the cylinder.

This drawing uses the Elephant figure from a set of hand-digitized representational images. The full set consists of: Goose, Frog, Fat Cat and Elephant. I often used these interchangeable figures in my early works. Digitized representational image of an Elephant is placed at intervals along a space curve. Curves generated by a mathematical function written by Christopher Scussel. The Elephant’s scale and orientation is based on data from the curve. The slope of the curve at a given point determines the direction of the bird figure. This is an early example of Generative Art. Many curves were drawn before this particular curves’ data set was determined. In essence, random to a point of being chosen by the artist.

This drawing uses the Frog figure from a set of hand-digitized representational images. The full set consists of: Goose, Frog, Fat Cat and Elephant. I often used these interchangeable figures in my early works. Frog Pond is an original work from around 1975. It is a very simple algorithm. A predetermined number of digitized frog figures are distributed about a center point using a random angle (0 – 359degrees) and radius. (a random polar coordinate) Then, at that location the frog image is rotated a random angle (0 – 359 degrees) Unique to this piece I used a plotter alphabet I designed, called Kolobet, to title the drawing.

This drawing uses the Goose figure from a set of hand-digitized representational images. The full set consists of: Goose, Frog, Fat Cat and Elephant. I often used these interchangeable figures in my early works. Geese is an original work from around 1975. The computer generates an array of translation coordinates and translates each goose into position. A mathematical function written by Christopher Scussel provides the rotation angle for each instance of the goose in its respective position in the array. The function provides difference rotation information and the overall flow of the image or surface pattern changes. Birds of a feather indeed flock together. This is an early example of Generative Art. Many versions were drawn before this particular data set was determined. In essence, random to a point of being chosen by the artist.

Horizons was an image intended as a wedding present for friends. The couple were Mormons and seagulls had some significance in their faith. At the time I wasn’t quite sure what marriage was about but it seemed to me that it was about a commitment to move off as a couple into the future. To me the future lies on the horizon. A random number of seagull figures are randomly distributed on horizontal lines. The spacing between each line of seagulls is determined by mathematical function. The function also determines the scale of the seagulls on each line. The function is visual below as lines distributed on a quarter cylinder. A mirror image. The viewer is drawn unknowingly to the horizon (into the future) which lies between the converging curved surfaces.

Hard to believe these to images have survived so long. The printer was one of the first computer output devices. When you ran a program on a computer in the early 1970’s you always got the output on printer paper. The was cheap and plentiful. Historically, some of first computer graphics were printer output made by arranging alphanumeric characters on printer pages. Computer nerds would figure out which characters to print to make Snoopy or Star Trek characters. They also figured out how to produce gray scales by overstriking characters. It was crude but effective. I was majoring in Graphic Design in the early 1970’s and with the help of my friend Chris Scussel, a math/computer science major. We tried to seriously push this medium to produce algorithmic art. He developed a kind of gray scale and we experimented with some functions. The result of which were these two drawings.

Hard to believe these to images have survived so long. The printer was one of the first computer output devices. When you ran a program on a computer in the early 1970’s you always got the output on printer paper. The was cheap and plentiful Hard to believe these to images have survived so long. The printer was one of the first computer output devices. When you ran a program on a computer in the early 1970’s you always got the output on printer paper. The was cheap and plentiful. Historically, some of first computer graphics were printer output made by arranging alphanumeric characters on printer pages. Computer nerds would figure out which characters to print to make Snoopy or Star Trek characters. They also figured out how to produce gray scales by overstriking characters. It was crude but effective. I was majoring in Graphic Design in the early 1970’s and with the help of my friend Chris Scussel, a math/computer science major. We tried to seriously push this medium to produce algorithmic art. He developed a kind of gray scale and we experimented with some functions. The result of which were these two drawings. Historically, some of first computer graphics were printer output made by arranging alphanumeric characters on printer pages. Computer nerds would figure out which characters to print to make Snoopy or Star Trek characters. They also figured out how to produce gray scales by overstriking characters. It was crude but effective. I was majoring in Graphic Design in the early 1970’s and with the help of my friend Chris Scussel, a math/computer science major. We tried to seriously push this medium to produce algorithmic art. He developed a kind of gray scale and we experimented with some functions. The result of which were these two drawings.

Kolomyjec’s Moiré was my attempt at making an Algorithmic Art contribution to the Op Art Movement. It is a mandala-like image that seems to pulsate as you observe it due to the Gestalt phenomena of figure-ground. Twelve equal-length, equal-spaced lines radiate from the center. The ends of these line split into 2 and radiate out a distance. (24) At the end those lines 3 lines split out a distance. (72) At the end those lines 4 lines split out a distance. (286) At the end those lines 5 lines split out a distance, so that at the final perimeter the circle is divided into 1430 points. This was a real testament to the quality and precision of the plotter equipment I was using in the day. (Calcomp 936)

le Morté de Beardsley is a carefully designed image. I wanted to pay homage to Aubrey Beardley based on a Dover book of his illustrations. I was very inspired by his illustrations and wanted to introduce some of his style into my nascent medium. I found this a google about the book: It was Beardsley's first major commission, and included nearly 585 chapter openings, borders, initials, ornaments and full- or double-page illustrations. The majority of the Dent edition illustrations were reprinted by Dover Publications in 1972 under the title Beardsley's Illustrations for Le Morte Darthur. Aubrey Beardsley died at age 23. le Morté de Beardsly is based on the illustration of a peacock. I was getting better at programming, so I tried a few things with this image. Some of the image was digitized by hand. That data was used to attempt a hidden line algorithm that did not render the lines behind the peacock’s neck. I had to carefully computer those intersections. The key to the image is the peacock’s eye. All the feather designs align to the eye of the peacock always returning the gaze of the viewer back to the eye. This had to calculated and adjusted by another algorithm.

A regular grid of square tiles. Each tile consists of a square with its perimeter divided into the same number of points of the circle it contains. Randomness determines the placement of the circles’ center relative to the center of the square. The method the points between the two shapes are connected create a 3D illusion.

The is regular grid tessellation made up of 9 column x 7 rows of tiles. Each tile is an interpolation between a smaller inner square and the larger outer square that contains it. The number of in-betweens in this variation is random. The position the small, contained square is allowed to vary (translate) horizontally and vertically by controlled randomness.

The scorpion is a hand-digitized figure taken from a woven rug purchased on a vacation to Greece. Later in graduate school I used the image from the rug as subject matter for this generative art piece. A computer algorithm used the digitized scorpion image data in a controlled random way. Instances are randomly distributed in rows, the algorithm decides, again randomly, whether to spin or not spin an instance of the image. If it chooses to spin the image it rotates it some number of random degrees as it scales the iteration. Creating tone or value in the overall image was a major objective. In plotter art imagery where you could only draw a line, the only way to create tone or value was by overdrawing an image. As a side note, both my wife and I were Scorpio’s. This piece suggests how Scorpio’s interact.

This is an early work. It is a regular grid tessellation where each “tile” consists of two randomly generated overlapping ellipse shapes. Each shape is made it of the same number of points. Rather than connecting the points (coordinates) that define the ellipse shapes’ perimeter, I connect one ellipses’ perimeter points to the corresponding point in the second ellipse and so on. This seems to create imaginary cylinders and a shallow perspective effect.

This is a simple regular grid tessellation; the tiles are either a twinkling star or a moon in one of its phases from full to almost new. A coin-toss algorithm is employed to decide on which shape is drawn. If the star is chosen then controlled randomness determines a star’s inner radius, the outer radius being fixed. That is as close as I could get to making a star twinkle. Then I rotate the star some random angle. If the moon is chosen, then controlled randomness determines the phase from full to almost new and some degree of rotation. One-twenty-eighth of the time no moon is drawn representing the new moon phase. The larger the overall image, is the more it represents the night sky.

M.C. Escher demonstrated this algorithm by employing traditional media and interlocking figures in his “square limit” graphic works. I don’t claim to be on par with Escher but I had a computer to do my drawing. I devised an algorithm (described below) and designed two interlocking hand-digitized figures: an angel representing good and a bat-devil representing evil. The image is designed to be hung on a 45 degree angle to keep these forces in balance. Ambiguity of Limits is a very specific form of spatial organization. All math and no randomness involved. The idea is that central figures are surrounded by half size versions of themselves. In turn that ring of shapes is surrounded again by half size versions of those figures, etc. In theory this could go on forever and you would never reach the outer limit. However, a practical limit is reached, and the process stopped when the area to draw the scaled version of the figure is smaller than the nib of the pen.

I already had a hand-digitized figure of a Seagull so I designed and hand-digitized the figure of a Walleye. I wanted to do a bird-fish transformation. I created a different kind of algorithm for changing one image into another where I stored all the line segments that make up an image (in this case two, the Walleye and the Gull) into two arrays. Think of it as deconstructing the figures and putting their component line segments into two piles. Then, over the course of some number of frames (numFrames) I juxtapose one image on the other. For one frame I build one image, randomly picking out a percentage of the line segments from one pile(1/ numFrames). Then I overdraw the second image, complete at first by in subsequent frames subtracting some number of line segments from the pile. For example, for an 11-frame sequence: First frame 100% of image one, 0% image 2. Second frame 90% of image 1, 10% of image 2. Third frame 80% of image 1, 20% of image 2. Until frame 11, 0% of image one, 100% image 2.

This was a proof of concept drawing of an algorithm I created for changing one image into another where I stored all the line segments that make up an image (in this case a set of vertical and horizontal lines) into two arrays. Think of it as of two bags of line segments. Then, over the course of some number of frames (numFrames) I juxtapose one image on the other. For one frame I build one image, randomly picking out a percentage of the line segments (1/ numFrames). Then I overdraw the second image, complete at first by in subsequent frames subtracting some number of line segments. For example, for an 11-frame sequence: First frame 100% of image one, 0% image 2. Second frame 90% of image 1, 10% of image 2. Third frame 80% of image 1, 20% of image 2. Until frame 11, 0% of image one, 100% image 2. I used this algorithm as the basis for my work entitled: That Walleye Has Got a Lotta Gull.

This was a surprising variation one of my earliest Generative Art pieces Organic Illusion Organic Illusion is a regular grid of square tiles. Each tile consists of a square with its perimeter divided into the same number of points of the circle it contains. Randomness determines the placement of the circles’ center relative to the center of the square. The method the points between the two shapes are connected create a 3D illusion. Twist uses the same configuration of a circle in a square divided into the same number of points. This time the circle is not randomly translated rather it is fixed in the center of the square. The coordinates that make up the sides of the square and the perimeter of the circle are stored in arrays. Using a linear interpolation technique to move from one point of a figure to the other I manipute the array indices of the circles’ data producing a happy but unexpected result. Twist is a true Op Art piece. It messes with your mind. If you try and hung it on the wall it always looks crooked.

A variation of Banana-Cone. Linear interpolation between two digitized representational images. One figure, the bunch of grapes, is placed inside the other, the water droplet. The outline of the water droplet is not continuous rather it is made up of the same number of points as the grape figure. I.e., carefully contrived. Linear interpolation is used to transform one figure to the other drawing in-between at intervals based on a function. What was interesting to me is how a third image appears from the transformation process in the form of a chalice.

A regular tessellation of overlapping “tiles.” The tiles alternate. The form of the tiles are two are variations of a circle. Each circle is comprised of vertical or horizontal line segments which are clipped by the outline of a circle. The line segment spacing, or intervals, are determined by a trigonometric function. This piece was originally called “spots” but over time has come to be known by a more descriptive name that reflects the gestalt interaction of the spots. A visual whole that has become more than the sum of its parts. Indeed a woven memory for me.