The Turtle graphics system in Python is built on the Tk interface and is a great logical shortcut to drawing the kind of patterns we are going to create.

Today we will review a simple flow chart description of an L-System, a way to model natural growth, and then proceed to a live coding exercise in which we will use string manipulation to model algae growth.

In this lecture we will combine what we've learned in the prior L-System and turtle graphics lessons to create the Koch curve. This curve, published in 1904 by Helge Koch opens up the general possibility of creating fractals through simple L-System interpretation.

Some facts about the perimeter, area, and dimension of the Koch snowflake.

We will now use the L-System approach to construct a simple, non-intersecting dragon curve. This serves as an example of how extensive the replacement method can be and how easily the code we wrote in Koch.py can be recycled into other fractals.

In this lecture we are expanding on our prior code for the simple dragon fractal to create the Jurassic Park dragon curve, which is our first space-filling fractal. At the same time we are dividing the script into two sections

1. A generalized function for creating fractals in turtle graphics
2. A main method created in a style that is standard for Python projects

As a brief break from our L-System creation we create an iconic fractal using recursion in Turtle graphics. The Serpinski triangle can be created in a number of ways and we will see it again as we continue to look at L-Systems and later as we delve into Cellular Automata.

In this lecture we will learn how to stack turtle states, essentially adding a recursive element into our iterative L-System, and use it to create a simple fractal plant.

We will take the next step in our L-System approach to modeling growth by adding a recursive aspect to our system which allows for branching patterns to occur and is great for creating trees and bushes.

At this point we can show how these growth algorithms can be used to fill space and create Fractal patterns that are fully two-dimensional.

We will revisit the creation of the Seirpinski triangle using L-Systems, also called the Seirpinski's Arrow system.

In this lecture we understand the concept of a Cellular Automata and perform a simple print based automata operation.

At this point we get more sophisticated in our printout and implement Rule 30, a specific one-dimensional automata.

This is the first part of our creation of the Game of Life automata in which we use the Tk interface to create a grid for two-dimensional automata creation.

In this lecture we finish our creation of the Game of Life, applying the rules of the game on our grid and observing what happens as we run it.

Using the same grid from the Game of Life, we now implement a set of rules called Majority Rule and observe the output.

In this lecture we expand on the Feigenbaum plot just created to add some event driven process items to zoom on different values for the a parameter.