Fractals in Clojure - Sierpinski Triangle
This fractal is called the Sierpinski triangle, after the Polish mathematician Waclaw Sierpinski.
Construction
In order to generate it we'll use the following algorithm,
- We pick a triangle on the surface.
- We shrink the triangle to half the height and width, make three copies, and position the three triangles so that each triangle touches the two other triangles at a corner.
- We repeat the above step until required depth is reached.
Code
(defstruct point :x :y)
(defstruct triangle :left :rigth :bottom)
We need two structures for representing a point on the canvas and the triangle we are drawing.
(defn midpoints [trig]
(struct triangle
(struct point
(int (/ (+ (:x (:bottom trig)) (:x (:left trig))) 2 ))
(int (/ (+ (:y (:bottom trig)) (:y (:left trig))) 2 )))
(struct point
(int (/ (+ (:x (:rigth trig)) (:x (:bottom trig))) 2 ))
(int (/ (+ (:y (:rigth trig)) (:y (:bottom trig))) 2 )))
(struct point
(int (/ (+ (:x (:left trig)) (:x (:rigth trig))) 2 ))
(int (/ (+ (:y (:left trig)) (:y (:rigth trig))) 2 )))))
Given a triangle this function will return a new triangle thats half the original triangle.
(defn create-triangles [trig step depth g]
(paint-triangle g trig)
(let [points (midpoints trig)
left (struct
triangle (:left trig) (:left points) (:bottom points))
rigth (struct
triangle (:rigth trig) (:rigth points) (:bottom points))
top (struct
triangle (:bottom trig) (:rigth points) (:left points)) ]
(if (< step depth )
(do (create-triangles left (inc step) depth g)
(create-triangles rigth (inc step) depth g)
(create-triangles top (inc step) depth g)))))
create-triangles is a recursive function that will call it self until required depth is reached. It first draws the given triangle then calculate 3 smaller triangles that will be placed inside the parent triangle.
Download code