Mandelbrot

This is a very simple, and not optimized, rendering of the mandelbrot set. Consider a sequence of complex numbers defined by \[ z_{n+1} = z_n^2+c \text{ where } z_0 = 0 \] for some constant $c$. Depending on the constant $c$, the sequence will either diverge or not. In the picture above, the cursor position $(x_m,y_m)$ is represented as a complex number $z=x_m+i y_m$ which corresponds to the complex number $c$. A white line (starting from $z_0=0$) is drawn between each point $z_n$ to the next $z_{n+1}$ during the iteration. If the sequence starts to diverge ($|z_n|\geq 2$) the sequence is terminated and the number $n$ is stored. The number $n$ then determines the color of that point according to some arbitrary cycle of colors. If it never starts, it is colored black. The image resulting from doing this at every point is displayed.

You can move around in the complex plane by mouse-dragging. Sorry... I did not bother to optimize the code very much, so at every re-rendering of the image you may have to wait a little while. How long you need to wait depends on your machine and how much you've zoomed your browser. You can also use the UP and DOWN arrows to zoom in and out respectively. Know, however, that this code does terminates at a certain maximal $n=n_{max}$. Therefore, there will be a "bottom" in the simulation. Upon reaching the bottom, please remember not to judge the mandelbrot set by the mistakes in this code. The mandelbrot set does not have a bottom.