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(ns ising-model.core
(:require [quil.core :as q]
[quil.middleware :as m]))
(defn setup [size]
"Setup the display parameters and the initial state"
(q/frame-rate 300)
(q/color-mode :hsb)
(let [matrix (vec (repeatedly (* size size) #(- (* 2 (rand-int 2)) 1)))]
{:grid-size size
:matrix matrix
:beta 20
:intensity 10
:iteration 0}))
(defn get-neighbours [state idx]
"Return the values of a cell's neighbours"
[(get (:matrix state) (- idx (:grid-size state)))
(get (:matrix state) (dec idx))
(get (:matrix state) (inc idx))
(get (:matrix state) (+ (:grid-size state) idx))])
(defn hamiltonian [state]
"Compute the Hamiltonian of a configuration state"
(- (reduce + (for [i (range (count (:matrix state)))
j (filter some? (get-neighbours state i))]
(* (:intensity state) ((:matrix state) i) j)))))
(defn toggle-state [state i]
"Compute the new state when we toggle a cell's value"
(let [matrix (:matrix state)]
(assoc state :matrix (assoc matrix i (* -1 (matrix i))))))
(defn delta-e [state i]
"Compute the energy difference introduced by a particular cell"
(* (:intensity state) ((:matrix state) i)
(reduce + (filter some? (get-neighbours state i)))))
(defn update-state [state]
"Accept or reject a new state based on energy
difference (Metropolis-Hastings)"
(let [i (rand-int (count (:matrix state)))
new-state (toggle-state state i)
alpha (q/exp (- (* (:beta state) (delta-e state i))))]
;;(println (hamiltonian new-state))
(update (if (< (rand) alpha) new-state state)
:iteration inc)))
(defn draw-state [state]
"Draw a configuration state as a grid"
(when (zero? (mod (:iteration state) 50))
(q/background 255)
(let [cell-size (quot (q/width) (:grid-size state))]
(doseq [[i v] (map-indexed vector (:matrix state))]
(let [x (* cell-size (rem i (:grid-size state)))
y (* cell-size (quot i (:grid-size state)))]
(if (= 1 v) 0 255))
(q/rect x y cell-size cell-size)))))
;;(when (zero? (mod (:iteration state) 100)) (q/save-frame "img/ising-######.jpg"))
(defn mouse-clicked [state event]
"When the mouse is clicked, reset the configuration to a random one"
(setup 100))
(q/defsketch ising-model
:title "Ising model"
:size [300 300]
:setup #(setup 100)
:update update-state
:draw draw-state
:mouse-clicked mouse-clicked
:features [:keep-on-top :no-bind-output]
:middleware [m/fun-mode])