Notes about Desmos

Newton's Basin Fractal

In the Desmos Graphing Calculator, turn on Complex Mode. Paste in the following:

f(z)=(2*z+1/z^2)/3
D=f(f(f(f(f(x+iy)))))
\operatorname{real}(D)>0
\operatorname{real}\left(D\right)\le0\left\{\operatorname{imag}\left(D\right)>0\right\}
\operatorname{real}\left(D\right)\le0\left\{\operatorname{imag}\left(D\right)\le0\right\}

I like the way that the boundary loops and curls around. Feel free to adjust the default colours, but you often lose the dark boundaries. I have not worked out why there is not a dark line on every boundary.

Custom Colours

Try this, which adds yellow to your palette:

y_{ellow}=\operatorname{rgb}(255,255,0)

To find out what red/green/blue (rgb) values to use, there are many colour pickers online, for example the colour picker at W3Schools, or use the one in Paint if you run a Windows computer.