I’ve been working on a shape grammar that generates a sequence that can then be run through a genetic algorithm. These images were generated using two shapes and a simple set of rules. Parameters of the rules are randomized when the composition is created and saved to a sequence that will be later be integrated into a genetic algorithm.
The spirographs above were created by a genetic algorithm. A collection of 36 compositions is generated at random and placed (by me) into three categories: top, mid, and bottom tier. Pulling most often from the top tier, second most from the mid, and least often from the bottom tier, a random sample of compositions (allowing for duplicates) is drawn from the 36. These selections are carried forward to the next generation. Within each new generation, individual compositions trade some of their parameter values (genetic code) with another composition and then some random mutations are inserted. The code-swap provides cross polarization, allowing attributes to be shared among the population. Mutations inject new twists, sometimes favorable, sometimes not so much. The resulting 36 compositions are then viewed and sorted to evolve the next generation.
Typically, in a genetic algorithm, an automated scoring algorithm would determine the fitness of each composition. The human involvement in the process allows the evolution to proceed more editorially.
It is a quick way to visually search through a parameter space. By selectively upvoting compositions of interest, one can create a population with variations on themes of interest. The process is a collaboration between algorithms, tools, and the composer.
For a while now, I’ve wanted to draw some of my line drawings onto large format paper and I’ve finally built myself a vertical plotter. There are several great tutorials online for building plotters that suspend a drawing gondola from two motors, use polar coordinates to control how the gondola travels, and a servo motor to raise and lower the pen. The video below shows a complete test plot on my plotter.
Much of the inspiration for the design of the penelope’s gondola, came from MTvplot. Like MTvplot, I decided to use large bearings with attached arms that rotate around a central point where the pen is placed. Keeping the pen tip in the center like this increases the accuracy of the plot. As the gondola moves left to right, the body of the gondola tends to rotate a bit relative to the the paper (for example, due to cable drag). With the tip at the center of rotation, the tip remains in the same place as the body rotates. Below are images of the first version of my gondola which is missing the weight I added in a later version.
To be able to easily adjust the width of my the plot area, I designed the motor mounts to hang from some picture rails already in my space. Within these mounts, I included smaller bearings to apply pressure to the belt and help hold it in contact with the teeth of the pulleys. I saw a similar detail in one of the online examples, but I can’t find the reference again.
For the counterweights, I settled on using pennies and printed cylinders to hold them. One of the benefits of this approach is that I was able to easily tune the weight by adding and removing pennies. At first, I tried to weigh the gondola only using the bearings (v1 pictured earlier), but I found that they did not provide enough stabilization when the distance between the gondola and motors was greater (for example, the bottom third of my 18×24 inch paper). This resulted in some shaky lines when drawing tight curves near the bottom of the page. To improve stability, I added a cylinder to hold pennies to v2 of gondola.
To help hold the pen with the tip at the center of the bearings and, when possible, at an angle to let ink flow down, I created a general purpose guide. This guide, is useful for quickly testing different pens, but proved difficult to set up accurately. I then created specific inserts to hold pens I plan to use regularly.
update: STL files available on Thingiverse.
For the hardware needed to control the motors, I first started with these two tutorials: https://www.instructables.com/Vertical-Plotter/ and https://www.youtube.com/watch?v=T0jwdrgVBBc. I liked the simplicity of using the motor shield and Arduino Uno — plus I already had that hardware. In the end, I got it working, but the pen traveled too slow to be useful. A friend recommended PenPlotter which uses a board specifically designed for controlling 3d printers. With this hardware, the PenPlotter software and the Repetier firmware included in the PenPlotter repo, I was able to get penelope drawing well.
Hardware shopping list:
The PenPlotter software requires some plotter-specific settings. For my current installation, they are:
PenPlotter includes several options for rendering images as a line drawing, but I am using it to draw SVG files. I am using Processing to programmatically create the SVG files. With Processing, there are some default ways to export SVG. The first is to record all shapes that are draw to the screen. The second option is to create an SVG PGraphics object and draw into it. Both of these options work well for 2d shapes, but ignore 3d shapes. The third option is to use beginRaw and capture everything drawn to the screen, including 3d shapes. Unfortunately, this process breaks the 3d shapes into very short lines, each its own line object in the final SVG file. PenPlotter generates a pen down and up for each of these lines in the drawing, resulting in long plot time and ink bleed at the start and end of each line.
So far, I have found the best option is creating an SVG PGraphics object and manually converting 3d shapes to 2d shapes using the screenX and screenY functions. This gives me me the best control over when the pen lowered and raised. It also gives me the ability to more easily crop shapes fit within the page boarder.
In the past, I have used PGraphics to generate high resolution PNG files offscreen and then preview them onscreen at a lower resolution. For penelope, I expanded this approach, adding a second PGraphics object to draw 3d shapes into in order to extract screenX and screenY values to use to draw 2d shapes into a separate PGraphics object. I can then preview this drawing onscreen and adjust the composition to my liking. Once I have a version that I want to plot, an SVG PGraphics object is created to draw the same 2d shape data to export the drawing to an SVG file for PenPlotter.
I use Processing’s beginShape, vertex, and endShape functions to define my lines point-by-point. For each shape made this way, PenPlotter will lower the pen, draw a series of lines connecting each point and then raise the pen. This is an easy way to control when PenPlotter sends pen down and up commands to penelope.
I found that by setting the dimensions of the offscreen PGraphics object (in pixels) to 71.95 times the dimensions of my paper (in inches), the exported SVG file is the correct size to be drawn at the default scale of PenPlotter.
I’m pleased with the initial drawing results from penelope. I’ve run into some issues, but have been able to mitigate many of them. The overall accuracy of the lines is great.
I did have some issues, especially when drawing near the bottom of the page and when drawing curves consisting of many smaller lines. These issues included:
Below is another video, this one showing parts of 2 hour plot. If you’ve built a similar plotter and have tips for me, please leave them in the comments below.
Some more sample results from a drawing app I am working on that uses a genetic algorithm to generate drawing (click for higher resolution):
Above: face 1, Below: face 2 (same source image as face 1)
Above: one generation of faces (same source as face 1 and 2)
Above: face 3 (different source image), Below: landscape.
Some results from a drawing program I am working on that uses a genetic algorithm to refine the drawing style. Below is the first generation.
First Generation (above) and 4th (below)
4th (above) and 7th generation (below)
 The 7th generation (above) and the 16th image in that generation below. 
The effects of mutations in one generation of spirographs. Choosing only one graph to survive from the previous generation (not a natural thing to do) results in 36 offspring from the one graph. It is an good way to check the impacts of mutations in the genetic algorithm and has an interesting outcome. The parent graph is below.
This Spirograph algorithm is not a strict interpretation of the physical Spirograph device but it generates some very similar and interesting results. The basic algorithm is to blend three circular equations together. Specifically, for values of i from 0 to 2 pi, an x and a y value are generated with :
x = r1 * cos(nr1 * i + o1) + r2 * cos(nr2 * i + o2) + r3 * cos(nr3 * i + o3); y = r1 * sin(nr1 * i + o1) + r2 * sin(nr2 * i + o2) + r3 * sin(nr3 * i + o3);
In many ways, this is like having three lines of length (set as r1, r2, and r3) being placed end to end with each one rotated a given number of times (set as nr1, nr2, and nr3). Each of the rotations also can be offset (set by o1, o2, o3).
Two different graphs can be drawn in this way and each of those graphs can be duplicated by changing the number of iterations (o iterations would hide graph). Each iteration can be offset by an angle or have its radius scaled.
This study focuses on the wave algorithms used in this years eggbot drawings. The sketch supports importing an image, scans the brightness value and draws horizontal lines with vertical offsets based on variations in brightness. around any given sample point along the horizontal line.
