clear all

N=100;
X=linspace(0,1,N);
[x,y]=meshgrid(X,X);

phi=sqrt((x-1/2).^2+(y-1/2).^2)-1/8;

figure;
contour(x,y,phi,[0 0], 'k', 'linewidth',3)
daspect([1 1 1])
title('Initial Conditions for Pb. 1.1')

figure;
phi=sqrt((x-1/2).^2+(y-1/2).^2)-(1/4+(1/6)*sin(atan((x-1/2)./(y-1/2))));

contour(x,y,phi,[0 0], 'k', 'linewidth',3)
daspect([1 1 1])
title('Initial Conditions for Pb. 1.2')