The Barnsley Fern is a fractal named after the British mathematician Michael Barnsley who first described it in his book _Fractals Everywhere_. The fern is one of the basic examples of self-similar sets, i.e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction. Like the Sierpinski triangle, the Bar…

barnsley-fern.cljs

(ns big-bang.examples.barnsley-fern
  (:require  
    [jayq.core :refer [show]]
    [big-bang.core :refer [big-bang]]
    [enchilada :refer [ctx canvas canvas-size]]
    [monet.canvas :refer [fill-rect fill-style]]))
 
(def width (first (canvas-size)))
(def height (second (canvas-size)))
(def scale (/ height 10))
(def offset (/ width 2))

(def black-spleenwort [
      ;Cumulative 
      ;Probability  Co-efficients
      [0.01        [ 0.00  0.00  0.00  0.16  0.00  0.00]]
      [0.86        [ 0.85  0.04 -0.04  0.85  0.00  1.60]]
      [0.93        [ 0.20 -0.26  0.23  0.22  0.00  1.60]]
      [1.00        [-0.15  0.28  0.26  0.24  0.00  0.44]]])

(def initial-state [0 0])
 
(defn pick-coeffs [prob affine-transforms]
  (first
    (for [[cumulative-prob coeffs] affine-transforms
          :when (<= prob cumulative-prob)]
      coeffs)))

(defn apply-transform [[x y] [a b c d e f]]
  [(+ (* a x) (* b y) e)
   (+ (* c x) (* d y) f)])

(defn update-state [event world-state]
  (->>
    black-spleenwort
    (pick-coeffs (rand))
    (apply-transform world-state)))

(defn render-fern [[x y]]
  (fill-rect ctx {
    :x (Math/floor (+ offset (* scale x)))
    :y (Math/floor (+ height (* scale y -1)))
    :w 1 :h 1}))
 
(show canvas)
(fill-style ctx "green")

(big-bang
  :initial-state initial-state
  :on-tick update-state
  :tick-rate 1
  :to-draw render-fern)