## Fractals in Clojure - Sierpinski Triangle

This fractal is called the Sierpinski triangle, after the Polish mathematician Waclaw Sierpinski.

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.
(ns sierpinski
(:import (java.awt Dimension Polygon Color)
(javax.swing JFrame JLabel)
(java.awt.image BufferedImage)))

(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
(/ (+ (:x (:bottom trig)) (:x (:left trig))) 2)
(/ (+ (:y (:bottom trig)) (:y (:left trig))) 2))
(struct point
(/ (+ (:x (:rigth trig)) (:x (:bottom trig))) 2)
(/ (+ (:y (:rigth trig)) (:y (:bottom trig))) 2))
(struct point
(/ (+ (:x (:left trig)) (:x (:rigth trig))) 2)
(/ (+ (:y (:left trig)) (:y (:rigth trig))) 2))))

Given a triangle this function will return a new triangle thats half the original triangle.

(defn paint-triangle [g trig]
(let  [polygon (new Polygon)]
(doto polygon
(.addPoint  (:x (:left trig))   (:y (:left trig)))
(.addPoint  (:x (:rigth trig))  (:y (:rigth trig)))
(.addPoint  (:x (:bottom trig)) (:y (:bottom trig))))
(.drawPolygon g polygon)))

(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.

(defn draw [depth width height]
(let [image  (BufferedImage. width height BufferedImage/TYPE_INT_RGB)
canvas (proxy [JLabel] []
(paint [g] (.drawImage g image 0 0 this)))
graphics (.createGraphics image)]

(.setColor graphics Color/white)
(create-triangles
(struct triangle
(struct point 0 height)
(struct point width height)
(struct point (/ width 2) 0))
0 depth graphics)

(doto (JFrame.)