In this one you can't zoom very far but there's some intresting parameters to play with.

I was watching this video by 2swap and another one by same video author about looking about different parameter spaces of the same simulation. As a way to visually grasp how those parameters affected things, by seeding them with values from the x, y plane. And using color of that point as output

Anyway it looked fun and i wanted to look around in the fractal also. Some things of note:

• Parameters are stored in the URL, you can share links to what youre seeing
• As already stated, you really can't zoom super far, sorry. There's a limit of how precise numbers can be in the computer and we're hitting it pretty immediately. I fear the next step would invole some strange math to get around it and frankly i won't do it.
• This is handwritten html + js. You can save this to your computer and run it (though you might have to inline the two imports) or look at the source with ctrl+u
• About the Coordinate mapping scale, they nominally go from 0 to 1. It's a multiplier for how much the coordinate space should influence any of the Z, C, E variables.

That last part is interesting. It's what lets us use the coordinate space as a diagram into the function's behavior over two variables.

Each pixel in the fractal view computes the same function, and takes on a color based on the result. The function is essentially Z^E + C, all complex numbers - these are the main values you set in the GUI.

Our trick is to use the pixel x,y position on the screen as real and imaginary parts of a complex number, and then use that as input to the function. In essentiality, we're able to look at the result of a lot of different inputs simultaneously and see if there's patterns.

(Spoiler, there's patterns.)

Read also:

-- crystal/mythology

-- logistic map cobweb

My mothership:

-- sixey.es

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