Perhaps you want to plot something like this:
p = [1, 2^1, 2^2, 2^3, 2^4];
for j = 1:length(p)
f = @(x,y) abs(x).^p(j) + abs(y).^p(j) - 1;
fimplicit(f, [-3/2, 3/2, -3/2, 3/2])
hold on
end
hold off
grid on, xlabel('x_{1}'), ylabel('x_{2}')
axis square
title({'Unit circles in the $p$-norm'}, 'interpreter', 'latex', 'FontSize', 12)
text(0.25, 0.4, 'p = 1', 'FontSize', 9)
text(0.60, 0.60, '2', 'FontSize', 9)
text(0.75, 0.77, '4', 'FontSize', 9)
text(0.85, 0.88, '8', 'FontSize', 9)
text(1.00, 1.04, '16', 'FontSize', 9)
