Maths is smART

Yesterday, I posted a picture using maths that looked like an owl. Now, maths is full of surprises… when typing in the code I wasn’t quite sure what I would get and I was quite pleased to see what had been created. Here are a few accidental animals:

Canary

Fish

…maybe they are quite vague, what do you think?

I hope you like my owl, I will be posting more pictures like this…

points=linspace(0,2*pi,100);
clf
hold on
for i = points
    X = [];
    Y = [];
    t=linspace(0,2*pi,100);
    x = cos(i)+cos(t);
    y = sin(i)+sin(t).^2;
    set(gca, ‘ColorOrder’, [139 69 19]./255);
    plot(x,y)
end
hold off

If I was to ask you to draw a star I am pretty sure that you would draw one of two things. Most likely the classic five-pointed star that you had trouble learning in primary school because it consisted of one constant motion from start to finish. If not the more simple six-pointed star comprising of two equilateral triangles. But have you ever wondered what defines a star? Well I have and it got me searching and I found the following article on star polygons:

http://mathworld.wolfram.com/StarPolygon.html

It defines a star polygon as the following:

A star polygon {p|q} (with p,q positive integers) is a figure formed by connecting with straight lines every q^th point out of p regularly spaced points lying on a circumference.

Basically we can create a {p|q} star by using the following algorithm:

1. Draw p points placed evenly around a circle.
2. Choose any free point and connect a line to the point q places around the circle, do this until you end up back at your starting point.
3. Repeat step 2 until there are no more free points.

You could create a computer program to implement this algorithm but you would be an absolute geek… which I am! So I did and here are a few of my favourite stars created using the program. The code of this program will be followed shortly.

A 10,2-star

A 15,3-star

A 90,30 star.

A 100,50-star

A 100,45-star

A 300,145-star