A STEM Project: Coding Waclaw Szpakowski's Rhythmical Lines in TurtleStitch

Waclaw Szpakowski B13, 1926, Museum of Art in Lodz

Coded with TurtleStitch and embroidered with a Brother PE800 Embroidery machine.

Waclaw Szpakowski B6, Series B, 1924

Coded with TurtleStitch and embroidered with a Brother PE800 Embroidery machine.

Waclaw Szpakowski (1883-1973) was a Polish architect and engineer who designed abstract drawings with ink and grid paper.  He began his drawings at the age of 17 and refined them over his lifetime. His ink drawings have very precise properties with straight lines drawn at right angles to one another which never intersect. Szpakowski created his drawings with lines that were 1mm thick and 4 mm apart. The ink drawings take on a rhythmical pattern starting on the left side of the page and ending on the right side. The movement of each design creates a maze of lines. The viewer of his drawings will ponder how the drawing were created by following the lines with their eyes to see where the line will take them. Where is the repeat in the pattern? Is the pattern flipped or was it repositioned? The patterns have a lot of movement in them and as a result, optical illusions of different patterns can be seen.

Waclaw Szpakowski published an album of sketches when he was 85 years old called "Rhythmical Lines"which displays the simplicity of the line and the geometric relationships between the lines. He described his works as "drawings of linear ideas" and by viewing his works, it shows the visual harmony of the "mathematical order of the universe" which includes symmetry and rhythmical balance. 

I coded a few of Waclaw's Szpakowski's designs in TurtleStitch and decided that I could create a basic TurtleStitch template to code Szpakowski's drawings because I used the same commands repeatedly. Here is the template that I created. https://www.turtlestitch.org/run#cloud:Username=Elaine&ProjectName=Waclaw%20Szpakowski%20Basic%20Commands 

The basic template that I created includes the following:

+ A size(scaling) factor and a width variable so that the design can be resized easily for embroidery with different hoop sizes. 

+Variables with basic values. In my early attempts to code Waclaw's designs, I used mathematical equations to move the turtle.  Subsequently, I determined that it is easier to have a set value for the turtle to move because of debugging. It is easier to see where the incorrect value is without having to do a computation.

+ Many of Waclaw's patterns are repeated from left to right across the design and a block command can be written for the code. By pointing the turtle in the upward position (point in direction 0), the block can then be repeated or flipped easily.

+ I created two simple turn and move blocks for the turtle, a "Turn Left 90 Degrees"  block and a "Turn Right 90 Degrees" block. Both of these blocks turn and move the turtle in their corresponding direction and allow for resizing and flipping. I used a flip factor equation so that the design can be flipped and the TurtleStitch code can be reused by assigning a flip value. 

Before I explain my flip factor equation, I will explain how an object is flipped over the y-axis. 

When an object is flipped over the y-axis from Quadrant I to Quadrant II, the x value changes from a positive value to a negative value.  The y value remains the same. 

This fact holds true when an object is flipped in code. I created an equation that will flip a point from a positive location to its negative location. Since all of the turtle movements are at right angles or 90 degrees to one another in Waclaw's designs.  A simple equation can be made to turn the turtle.

Turn Right 90 Degrees

I created the above "Turn Right 90 Degrees" block to turn the turtle to the right. There are two variables, "flip1" and "flip2" which determine the location of the turtle.  (Please note that the steps and size factor variables in the equation determine the distance and scaling factor that the turtle will move.)

Unflipped Position 

The "flip1" variable must be a 1 and the "flip2" variable must be a 0 for the turtle to turn to its "unflipped" position of 90 degrees.

The "flip1" variable must be 1 for the turtle to move to its "unflipped" position.

Flipped Position

When flipping the turtle, it must move 180 degrees to achieve the flip plus the original 90 degrees for the turn.  The "flip1" variable must be -1 and the "flip2" variable must be 360 for the turtle to turn to its "flipped" position of 270 degrees. 

The "flip1" variable must be -1 for the turtle to move to its "flipped" position.

Turn Left 90 Degrees

 The "Turn Left 90 Degrees" block is coded exactly the same way but with the turtle will turn to the left.

Using this code, I recreated seventy of Waclaw Szpakowski's works in TurtleStitch. https://www.turtlestitch.org/projects/g/search/waclaw%20szpakowski. 

I did this by copying each of Waclaw's Szpakowski's designs and placing it in the Silhouette software. Whereby I was able to resize and overlay a series of blocks on top of each design.  I was then able to determine the numbers of steps needed to complete each line by counting the blocks and coding it using the "Turn Left 90 Degrees" and "Turn Right 90 Degrees" blocks.

In the following photos, I exported the coded images as an SVG in TurtleStitch and copied it into the Silhouette Cameo software where I was able to print the designs using an ink pen and Foil Quill on 65 lb. cardstock.

Ink Pen

Ink Pen

Ink Pen

In the example above,  I used a Foil Quill Heat Pen with the Silhouette Cameo. A metallic film is placed on top of the cardstock and the Foil Quill Heat Pen fuses the metallic foil onto the cardstock wherever the pen tracks the design.