% there is more than one way to make a 4-ball

figure(1)
t = -1:2/500:1; [x,y] = meshgrid(t,t);  spy(x.^4+y.^4<1,'k.'), axis equal, axis off
figure(2)
x = -1:0.01:1; scatter(x,(1-x.^4).^0.25); hold, scatter(x,-(1-x.^4).^0.25); hold
figure(3)
x = -(-128:128)/128; y=(ones(1,257)-x.^4).^0.25; area(x,y); hold, area(x,-y); hold
figure(4)
x = -1:.01:1; fill(x,(1-x.^4).^(1/4)), hold, fill(x,-(1-x.^4).^(1/4)), hold
figure(5)
t = -1:2/500:1; [x,y] = meshgrid(t,t); contourf(x,y,x.^4+y.^4,1), axis equal, axis off
figure(6)
for i=1:1000, x=randn(2,1); x=x/norm(x,4); plot(x(1),x(2),'.'); hold on, end, hold off
figure(7)
x = repmat(-1:0.01:1,201,1); f = @(x,y)(x.^4+y.^4); contour(f(x,x'),1), axis off