Using Euler Math Toolbox with the plotting function given at the end of this article, I did a search for the rightmost points of the Mandelbrot sets. My candidate for the rightmost points are in the neighborhood of 0.4708247 + i*0.3478550 (and its conjugate). Not sure what the significance of those values is.

function Mandelbrot(a,b,c,d,n=500,m=100)

z=linspace(a,b,n)+1i*linspace(c,d,n)’;

h=zeros(size(z));

loop 1 to m

h = z + (h)^2;

h=(abs(h)>10)*10+(abs(h)<=10)*h;

end

density(log(max(abs(h),1))>0.001);

setplot(a,b,c,d);

xplot();

return h;

endfunction