I finished reading Chaos and Fractals a few days ago. If you’re looking for a good introductory book on fractals and chaos that doesn’t shy away from mathematics, I highly recommend it. I read the book straight through from cover to cover, and while there are still quite a lot of topics I don’t understand and will be referencing the text quite a bit in the next while, it was good to get an overall view of the field.
Koch Curve
I started to write a few programs to explore the topics covered in the book. One of the earliest fractals described is the Koch curve, named after the Swedish mathematician Helge von Koch.
The curve has many interesting properties, one of which being that its length is infinite. Additionally, while it is continuous everywhere, it is differentiable nowhere.
I wrote a quick sketch in Cinder to create the Koch curve. Of course, being a mere representation, it’s not a real fractal, but it at least gives you an idea of what the curve looks like and the program does use iterations to generate the shape.
Koch Snowflake
Combining three Koch curves, one can create the Koch snowflake, shown below.
The programs are pretty simple, and I wrote them mainly just to get the structure of the iterations down. I’m be exploring variations of the Koch snowflake the next few days, and finding ways to add color to the shape. I’ll also be exploring 3D structures that follow the same properties.