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

Julia Set Gif

     I decided that the best way to show fractals is through gifs. This involved around 2 hours of screenshots and waiting so I think next time
I will find a better way to create a gif.
     This Julia Set comes not from z = z^2 +c, but z = (z^4+c)/z I can divide by z because it doesn't start at 0 as it is a Julia. I am traversing from c = -2 to c = 0.55. I needed to stop somewhere. Also, I skipped a lot between the second to last frame and the last frame.

If the gif doesn't display which is practically inevitable  highly improbable, despite considering the fact that it dances before my eyes as I type this, click this link

The Dragon Curve

     The dragon curve is a beautiful fractal with a great deal of interesting properties. The two main ways I know of to make it are breaking down lines and copying an image and adding it 90 degrees from the starting image.

         I prefer the first method. You start out with a line. Every line present in any iteration is split up into two lines of equal length a little smaller than the first one. The two new lines form a right triangle with the line they came from and the line they came from is erased. Since a line has two sides, each set of new lines could go on either side; to make the dragon curve the new lines must go on the appropriate side. For a while my program made triangles instead of dragon curves when it was dragon curves I wanted. this awesome youtube video helped me figure out what was wrong.  If you want an adequate explanation of the dragon curve go to This Amazing Website . I think about it as lines but the triangle method shows how things have to be done better. The website is super awesome I highly recommend it. I have made a variety of shapes by varying the technique for where the lines are drawn.

Dragon curve:

Miscellaneous creation

Triangle

     The nature of this particular algorithm is that each line becomes its own shape later on. In the dragon curve each line becomes a dragon. In the triangle each becomes a triangle. I suspect this isn't completely true for some of the weirder shapes because a line may be created in conditions differing from those of the original shape, but subsequent lines may be in those conditions. 

     This nuance means if the algorithm changes after a couple iterations, the established shape will end up composed of copies of the shape the new algorithm specifies.

Triangle of triangles (there are multiple ways to get triangles)

Triangle made of dragon curves

Dragon curve made of triangles

 Dragon curve made of smaller triangles

Some images of the madlebrot

Many of these photos depict the same area of the Mandelbrot set with different settings. It is interesting how the same shape can come in forms that look so different from each other.