Curve
Maurer Rose
Formula taken from Wikipedia . MATLAB code given below . Varying 'n' and 'd' in code give different curves.
n = 2;
d = 39;
k = (0:120)/180*pi;
[x,y] = pol2cart( k*d , sin(n*d*k) );
line(x,y);
axis equal off
n = 3;
d = 47;
k = (0:180)/180*pi;
[x,y] = pol2cart( k*d , sin(n*d*k) );
line(x,y);
axis equal off
n = 2;
d = 29;
k = (0:360)/180*pi;
[x,y] = pol2cart( k*d , sin(n*d*k) );
line(x,y);
axis equal off
n = 3;
d = 17;
k = (0:180)/180*pi;
[x,y] = pol2cart( k*d , sin(n*d*k) );
line(x,y);
axis equal off
Super Ellipse
Generalized formula for super ellipse is abs(x/a)^m+abs(y/b)^n=1,m>0,n>0. Formula taken from Wikipedia
% MATLAB Code
% m = 1, n = 2, a = 1, b = 1
ezplot('abs(x)^1 + abs(y)^2 - 1',[-1.5 1.5 -1.5 1.5]);
axis equal
% MATLAB Code
% m = 0.5, n = 5, a = 1 ,b = 1
ezplot('abs(x)^0.5 + abs(y)^5 - 1',[-1.5 1.5 -1.5 1.5]);
axis equal
% MATLAB Code
% m = 1.5, n = 1.5, a = 1 ,b = 1
ezplot('abs(x)^1.5 + abs(y)^1.5 - 1',[-1.5 1.5 -1.5 1.5]);
axis equal
% MATLAB Code
% m = 0.5, n = 2, a = 1 ,b = 1
ezplot('abs(x)^0.5 + abs(y)^2 - 1',[-1.5 1.5 -1.5 1.5]);
axis equal
Chrysanthemum
Formula taken from Paul Bourke website . MATLAB code given below .
u = linspace(0,21*pi,2000);
r = 5*(1+sin(11*u/5))-4*sin(17*u/3).^4.*sin(2*cos(3*u)-28*u).^8;
x = r.*cos(u);
y = r.*sin(u);
z = (r/20+0.2).*sin(r*2*pi/7);
figure
line(x,y,z);
axis equal off
view(3)
figure
verts = {[x' y' z']};
h = streamtube(verts,0.15);
shading interp,colormap(cool)
axis off equal
view(3)