Koch snoflake

The Koch snowflake is a classic fractal. It, like many other similar fractals, can be made a number of ways (IFS, Sierpinski hexagon, L systems, trees, more?). The usual way to make it is to draw an equilateral triangle, then for every line, draw a new equilateral triangle that has one edge along the middle third of the line. The process of replacing each line with a line that has a spike in the middle is repeated until you have the image below. I found the point of the added triangles by first finding the 2 points that separate the lines into thirds, then rotating the point that lies further counter clockwise and rotating it 60 degrees clockwise around the other point.

The modifications of the normal figure found here were made in several ways. Some where made by rotating the point counterclockwise rather than clockwise at varying times (e.g. every third triangle piece). Others were made by rotating it by different angles. One of the videos was made by varying things in a way I have not analyzed enough to understand; I believe it varied both angle and radius but if so it was done indirectly through rotation matrix shenanigans.

Koch

Anti-Koch

Video time!!!!

Some Newton Fractals and Images Made of Images

I like to pretend some day I will put explanations for the pictures I post. Its strange because I am always eager to explain them to people individually, somehow I feel obligated to formalise things if I explain them here and that feels boring and annoying. Feel free to ask me stuff through comments or email, I will be more than happy to answer.

Newtons Fractal

Not working yet

Still not working

The shape is almost right

The shape is right but it looks very different from what I have seen before

Getting closer to the standard

Very close but there's this weird bit at the bottom

This is what most look like.

It turned out that the program was having difficulties with 0 and 2pi.

My Favorite Julia Set

I found the equation for this particular Julia set type fractal on this website which is also linked to in my list of links. The equation is: (z^3+c)/z. The three gifs are colored using different algorithms.
My classic algorithm:

Credit to Eyob Tsegaye for helping me make the above gif

A very strange algorithm that completely ignores iterations and instead focusses on where Z goes during the iterations:

The same as the last one but with a cool effect:

Lines: Lots of Them; and a Mandelbrot

I almost lost sight of what this blog was supposed to be. This is ridiculous because I have barely posted, but nevertheless i forgot the true meaning of this blog. I make cool fractals and like showing them to people and this feels like a less obnoxious way of doing it. I make no promises of explanation, only of fractals.

Crazy mandelbrot shenanigans