Islamic-inspired art is a good starting point for explorations of geometry, symmetry, and tiling. In this workshop we will program different Islamic-inspired art pieces using ArtLogo. 

Using ArtLogo

You can type procedures and commands directly into ArtLogo: for this workshop we will work entirely in our browser. At the end of the workshop you can copy and paste the procedures you work on from ArtLogo into a text editor, like TextEdit or Notepad.

Here are what the different parts of ArtLogo are used for:

We will be writing procedures in the pane on the left and executing them from the Command center area at the bottom of the screen.

It is helpful to have the ArtLogo Reference open in another tab so you can refer to the syntax as you work.

Symmetry Through Rotation

Islamic art uses rotation of geometric shapes to create secondary shapes. We can program a polygon that we rotate to create symmetrical designs. Let's start by programming the turtle to draw a hexagon.

Type hexagon in the Command center to execute the procedure.

We can then write a master procedure called go that tells the turtle to draw a hexagon, rotate right (or left), and repeat that enough times for the turtle to turn a full 360°.

Let's add to the go procedure: we are going to clean the screen and hide the turtle before the design is drawn.

Further Ideas

Now that you understand how to draw and rotate, you can experiment with pen size and colors. We can create additional complexity in the design using these tools. Try running the procedure with a large pen size in one color then a second time with a smaller pen size and a different color.

You can also change the background color by filling the screen before the procedure run to emphasize the design.

Since we programmed this design in a "modular" fashion we can easily program a different polygon and swap it into our go procedure. Here is a heptagon.

At this point I am going to copy and paste my procedures into a TextEdit document and save the document.

Tiling

Another way Islamic art makes complex designs is through tiling a polygon with overlap. We can tile our hexagon (or heptagon if you wish) and create secondary shapes.

You need to know the extent of the xy axis in ArtLogo. Here are the coordinates.

Let's start by erasing the screen and putting the turtle in the upper left corner of the screen before drawing a polygon.

If we change the x coordinate a little and leave the y coordinate the same we can draw additional overlapping hexagons, like this:

The second part of the tiling is sending the turtle back to the left side of the screen and changing the y position like you did the x position. We are going to couch our x coordinate changing procedure inside the y coordinate changing procedure.

This design is good but not quite what I want. If we move the second row slightly to the left of the first row the overlapping will be more interesting. 

We can run this procedure twice with different pen sizes and colors. A dark background will make the colors stand out, too.

Again, I am going to take that tile procedure and paste it into a TextEdit document.

Play

Now take what you have learned about rotation and tiling and program your own procedures. Try running the procedures multiple times with different sized pens and different colors. Research a famous mosque and try programming some of the motifs found there, like the Alhambra design pictured at the top of this page or this design from the Mustansiriya Madrasah in Iraq.

Remember to copy and paste your procedures into a text document so you can return to the design later.

Assets

Alhambra procedure

Hexagon and Heptagon procedures

Mustansiriya Madrasah procedure