Symmetry with Turtle Graphics

In today’s MOO ChatShaala session, we discussed symmetry with reference to our encounters with symmetry and how Turtle can help us in visualizing symmetrical objects, explore various types of symmetry.
This conversation led to participants trying to figure out the meaning of simple Turtle code for themselves, and furthermore, creating an octagon with self-inspiration!
We tried to explore the octagon design further in order to draw a spider web, incidentally steering the discussion over to how does a spider know that it has to create a symmetrical web? Do humans too instinctively follow symmetrical motion? Or is it an acquired knowledge that symmetry is preferable? Does symmetry create equilibrium or balance?
However, we could not create an ideal symmetrical design using turtles today.
turtleweb-1st try
So today’s TurtleArt challenge is to create structure resembling to the expected design in drawings.
If you’re visiting the turtlechat first time today, you might like to try visiting and see if you can come up with a symmetrical solution by building upon blocks used in the picture!

We will be meeting again next week to workout the TurtleWeb challenge and explore symmetry further.


Today’s Turtle ChatShaala saw three interesting phases of solving the TurtleWeb challenge. Every participant tries to play with the turtle at the level of his or her own comfort. Thus, approaches of making the turtle move, repeat an action or a set of action, all differ from one another. Here are artworks by @Vaibhavi, @G_N and Anshika (@KiranyadavR) which went closer to a real Spider Web:
vaibhavi trial
Here, Vaibhavi has used approximation to determine beginning location for every iteration that we tried last week.
This week, we simplified this problem one step, to start with concentric squares first… moving ahead towards hexagons.
Anshika, tried out the in-class activity of drawing squares at her end and shared her artwork:
anshika image
I used the property of Hexagons, that in Hexagons, the radius is of same length as that of the sides, all angles are also equal, including the angle each side’s vertices make with the center. If you would like to go through my code, try it out on your own, go ahead!
You could also make it look more like a spiderweb by adding the vertices connecting string in this one.
A hexagon shaped spider web looks sort of like a jigsaw puzzle made up of connected equilateral triangles. This was observed keenly by GN who solved the challenge during our meet today!
@G_N came up with a generic solution:
He disintegrated the problem of drawing the whole hexagon into drawing concentrically placed equilateral triangles.
For next week, our questions are going to be:
Which types of symmetry can you spot in these designs? Can we make two separate turtles mirror each other? Can we make them create the same diagrams concurrently? Come up with your challenges aligned to this one for next week!