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%Celebrate spring by planting a flower in MATLAB ? Code ?

n=800;

r=linspace(0,1,n);

theta=linspace(0,2*pi,n);

[R,THETA]=ndgrid(r,theta);

% define the number of petals we want per cycle. Violets have 5!

petalNum=5;

x = 1 - (1/2)*((5/4)*(1 - mod(petalNum*THETA, 2*pi)/pi).^2 - 1/4).^2;

% update the formula for phi to stop the spiralling effect

phi = (pi/2)*exp(-2*pi/(8*pi));

y = 1.95653*(R.^2).*(1.27689*R - 1).^2.*sin(phi);

R2 = x.*(R.*sin(phi) + y.*cos(phi));

X=R2.*sin(THETA);

Y=R2.*cos(THETA);

Z=x.*(R.*cos(phi)-y.*sin(phi));

% color code for blueviolet RGB 138,43,226

% Indigo rgb value (75,0,130)

mapSize=20;

blue_map=linspace(138,75,mapSize)';

blue_map(:,2)=linspace(43,0,mapSize)';

blue_map(:,3)=linspace(226,130,mapSize)';

% and a pretty bit in the middle

gold_map=[255 215 0; 250 210 0];

% combine to form a full flower map

violet_map=[gold_map; blue_map];

% Now lets plot it and try and pick an attractive angle

surf(X,Y,Z,'LineStyle','none')

colormap(violet_map/255)

view([-12.700 81.200])