A Couple New Fractals

Ryan Baxter — Mon, 12 Jan 2009 12:46:00 -0800

I’ve created types for both the Burning Ship and Newton fractals and added them to trunk of the Ruby Fractal Library repository. The Newton fractal was a little tricky since its formula requires the derivative of a polynomial p(z). A private “derivative” method yields the results of the expression, (f(x + dx) - f(x)) / dx when dx is provided as a parameter and p(z) is passed to the block.

private
def derivative(dx)
  lambda { |x| 
    (yield(x + dx) - yield(x)) / dx 
  }
end

Before making an official release, I’m going to do a few creative things with blocks and add one or two new coloring algorithms.

After the release, I’d like to begin experimenting with iterated functions and random fractals in hopes of making the library more well rounded. I’m also thinking about abstracting the rendering logic in an attempt to make RMagick less of a dependency. We’ll see how that goes.

The following code was used to render the fractals seen here:

burningShip = BurningShip.new(Complex(-1.75, -0.04))
burningShip.magnification = 32
burningShip.save_as('burning_ship.png')

newton = Newton.new
newton.a = -0.5
newton.pz = lambda { |z| z**3 - 1 }
newton.theme = Themes::Winter
newton.save_as('newton.png')

Once that is all said and done I’ll be taking a break from fractals to work on another pet project. I’ll post more on that when I have something to show. Cheers.

crunchlife: A Couple New Fractals

A Couple New Fractals