So you give me a mathematical function, and I will make a fractal out of it!

You do not need to understand how Newton's Method works to make a request.

The rules:

- Be creative! A simple function (like f(x) = x
^{2}) might not produce anything interesting. More complicated functions may not produce anything interesting either, but I can adjust them to make them interesting. - You may use any of the following in your function:
- Any arithmetic: addition, subtraction, multiplication, division, in absolutely any combination.
- Imaginary numbers (represented by "i")
- Trigonometric functions: sin, cos, tan, etc.
- Inverse trigonometric functions: arcsin, arccos, arctan, etc.
- Exponentials: e^x, x^(-1/2), x^x, x^i, and so on.
- Logarithms
- Any, absolutely any combination of the above. Even something like x*(cos(tan(x))^(i/x))-log(i+arctan(x)) is possible. But please don't suggest anything that crazy.

Oh, and here's one more example to throw out there. This Mandelbrot look-alike was generated with the function (x+1)*sqrt(x).

I will post a bunch of these at a later date.

## 4 comments:

I'd like to see hyperbolic sine, cosine, etc.

Yep, you can see those too, although I should mention that they're not much different from the regular trig functions (because cosh(x) = cos(ix), sinh(x) = isin(ix) and so forth).

how about e^-(ixcosx)+e^(xsinx)

A bold request! But I like the results. Wait 'til you see.

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