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.)
      (.add canvas)
      (.setSize (Dimension. width height))
      (.show))))

(draw 4 400 400)

Sierpinski Triangle