Andy's blog

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Cayley graph 3D

Cayley graph 3D

I was in the keynote session of AAMT conference. In the keynote, the mathematician Hanna Neumann was mentioned. I immediately googled and started reading about her on Wikipedia.

While reading, my thoughts are like the hyperlinks that go everywhere, then suddenly I saw and clicked into the Group theory, where I found the Cayley graph that caught my attention.

It is easily recognisable that this cayley graph is a fractal image, which can be produced with a simple recursive procedure in VRMath2's LOGO language.

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12 Tables

12 tables

In this blog, I am trying to use an existing LOGO program in VRMath2 called table.logo, then see if I can create a couple of tables using repeat command.

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Recursive 2D fern leaf procedure

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In my previous blog, I explained about a recursive tree procedure. Here is another one borrowed from Joshua's Logo Interpreter example: fern leaf procedure. This fern leaf procedure creates a 2D fern leaf in VRMath2's 3D space. You can examine it below in the 3D space with the LOGO program.

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Recursive 2D tree

Recursive 2D tree

One of the powerful abilities of LOGO programming language is its recursive execution of procedure. Recursive call of procedure means a procedure calls itself until an exiting condition is met. A recursive procedure can be very simple yet it can produce complex and beautiful mathematical graphics such as fractal images and naturally occurring objects. 

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My first 3D project: A simple table

Simple table design

This table is consisted of 5 objects. The table top is a scaled box (cube). The four legs are scaled cans (cylinder).

To make this table, I carefully walked the turtle to the location where the objects should be placed and rotate the turtle to face certain direction before I place the objects. To move the turtle, I use the Quick Command Window to try first, and eventually I wrote in the Logo Editor Window the following commands to create this table.