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R5099/6_Spatial_simulation.html
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6_Spatial_simulation.html
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<!DOCTYPE html>
<html>
<head>
</style>
<script src="https://d3js.org/d3.v4.min.js"></script>
</head>
<body>
<script>
function draw_grid(data,colors) {
var width = 600;
var height = 600;
var grid_length = data.length;
var svg = d3.select('body').append('svg')
.attr('width', width)
.attr('height', height);
var rw = Math.floor(width/grid_length);
var rh = Math.floor(height/grid_length);
var g = svg.selectAll('g')
.data(data)
.enter()
.append('g')
.attr('transform', function (d, i) {
return 'translate(0, ' + (width/grid_length) * i + ')';
});
g.selectAll('rect')
.data(function (d) {
return d;
})
.enter()
.append('rect')
.attr('x', function (d, i) {
return (width/grid_length) * i;
})
.attr('width', rw)
.attr('height', rh)
.attr('class',function(d) {
return d;
});
if (!colors) {
d3.selectAll(".NoBacteria").style("fill","#fff");
d3.selectAll(".Bacterium").style("fill","#808080");
d3.selectAll(".Dead").style("fill","#C0C0C0");
}
else {
for (var i = 0; i < colors.length; i = i + 2) {
d3.selectAll("."+colors[i]).style("fill",colors[i+1]);
}
}
}
function update_grid(data,colors){
var grid_length = data.length;
d3.select('svg').selectAll('g')
.data(data)
.selectAll('rect')
.data(function (d) {
return d;
})
.attr('class',function(d) {
return d;
});
if (!colors) {
d3.selectAll(".NoBacteria").style("fill","#fff");
d3.selectAll(".Bacterium").style("fill","#808080");
d3.selectAll(".Dead").style("fill","#C0C0C0");
}
else {
for (var i = 0; i < colors.length; i = i + 2) {
d3.selectAll("."+colors[i]).style("fill",colors[i+1]);
}
}
}
// initiation of variables
// ------ Uncomment if called by "WebPage.html" ------
/*var params = location.href.split('?')[1].split('&');
var N = Number(params[0].split('=')[1]);
var division_rate = Number(params[1].split('=')[1]);
var killing_rate = Number(params[2].split('=')[1]);
var noise_division = Number(params[3].split('=')[1]);
var noise_killing = Number(params[4].split('=')[1]);
*/
// --------------------------------------------------
// ------Comment if called by "WebPage.html"--------
var division_rate = 1/150; //per minutes
var killing_rate = 1/150; //per minutes
var noise_division = 0.05; //per minutes
var noise_killing = 0.05; //per minutes
var N = 15; // initial population size
// --------------------------------------------------
var time_lapse_in_minutes = 1000; // duration of the simulation
var bacterium=[];
var growth_rates = [];
var grid_length=100;
var grid = [];
var cell=0;
var no_cell=0;
function init_grid(){
for (var i = 0; i < grid_length; i++){
grid[i]=[];
for (var ii = 0; ii < grid_length; ii++){
grid[i][ii] ="NoBacteria";
no_cell=no_cell+1;
}
}
for (var i = 0; i < bacterium.length; i++){
grid[bacterium[i].position_x][bacterium[i].position_y] = "Bacterium";
cell=cell+1;
}
console.log("InitialGrid: ");
console.log(no_cell, cell);
}
function get_bounded_index(index){
var bounded_index= index;
if (index<0){
bounded_index= index + grid_length;
}
if (index>= grid_length){
bounded_index= index - grid_length;
}
return bounded_index;
}
function random_between(min, max) {
return Math.floor(Math.random() * (max - min)) + min;
}
// create a new bacterium
function new_bacterium(time_since_div, posx, posy){
var divisionTime = 2 * (1/division_rate) + 1;
while (divisionTime < 20 || divisionTime > 2 * (1/division_rate) ) {
divisionTime = random_from_normal_distribution( 1/division_rate, noise_division * (1/division_rate));
}
var killingTime = 2 * (1/killing_rate) + 1;
while (killingTime < 0 || killingTime > 2 * (1/killing_rate) ) {
killingTime = random_from_normal_distribution( 1/killing_rate, noise_killing * (1/killing_rate));
}
var new_bact = {
individual_division_rate: 1/random_from_normal_distribution(1/division_rate , noise_division * (1/division_rate)),
individual_killing_rate: 1/random_from_normal_distribution(1/killing_rate, noise_killing * (1/killing_rate)),
time_since_division: time_since_div,
division_time: divisionTime,
killing_time: killingTime,
position_x: posx,
position_y: posy
};
return new_bact;
}
// kill a bacterium
function kill_bacterium(index,bacterium_to_kill){
grid[bacterium_to_kill[index].position_x][bacterium_to_kill[index].position_y] = "Dead";
bacterium_to_kill.splice(index,1);
}
//uses Box-muller transform to get normal random variables from uniform random variables
//https://theclevermachine.wordpress.com/2012/09/11/sampling-from-the-normal-distribution-using-the-box-muller-transform/
function random_from_normal_distribution(mean, variance) {
var u1 = Math.random(); // should belong to ]0,1]
if (u1 == 0){
u1 = 1;
}
var u2 = Math.random(); // should belong to ]0,1]
if (u2 == 0){
u2 = 1;
}
theta = 2 * 3.14 * u2;
var r = Math.sqrt(-2 * Math.log(u1));
var x = r * Math.cos(theta);
var y = r * Math.sin(theta);
x = mean + Math.sqrt(variance) * x;
// return only one of the two normal random variable generated
return x;
}
// calculate the population size for each time step
function next_time_step() {
//var next_N = current_N;
//var temp_bacterium = [];
/*if (bacterium.length!=current_N){
console.log("problem");
}*/
temp_bacterium = bacterium.slice(0); // creates a copy - not the reference of the array.
// var all_bacterium_to_kill=[];
for (var i = bacterium.length-1; i >= 0 ; i--){
//Divide cells with a frequency of "individual_division_rate"
try{
bacterium[i].time_since_division = bacterium[i].time_since_division+1;
if (bacterium[i].division_time <= bacterium[i].time_since_division){
var position = find_position(bacterium[i].position_x,bacterium[i].position_y);
temp_bacterium[i] = new_bacterium(0,bacterium[i].position_x,bacterium[i].position_y);
temp_bacterium.push(new_bacterium(0,position[0],position[1])); // division rate is not inherited
grid[position[0]][position[1]]="Bacterium";
//next_N = next_N + 1;
}
}
catch (err) {
console.log(i);
}
//kills cells with a frequency of "individual_killing_rate"
if (bacterium[i].killing_time <= bacterium[i].time_since_division){
// all_bacterium_to_kill.push(i);
kill_bacterium(i,temp_bacterium);
}
}
// kill them all at once otherwise the index changes
//for (var i = all_bacterium_to_kill.length-1; i >= 0 ; i--){
// kill_bacterium(all_bacterium_to_kill[i],temp_bacterium);
//next_N = next_N - 1;
//}
bacterium = temp_bacterium; //replaces the old bacterium table by the new one for the next time step
//return next_N;
}
function find_position(actual_pos_x,actual_pos_y){
var numdispo =0;
for (var x = -1; x <= 1; x++ ){
for (var y = -1; y <= 1; y++ ){
if (grid[get_bounded_index(actual_pos_x + x)] [get_bounded_index(actual_pos_y + y)] == "NoBacteria"){
numdispo++;
}
}
}
if (numdispo>0){
var myArray = [-1, 0, 1];
while (1){
var x = myArray[Math.floor(Math.random() * myArray.length)];
var y = myArray[Math.floor(Math.random() * myArray.length)];
if (grid[get_bounded_index(actual_pos_x + x)] [get_bounded_index(actual_pos_y + y)] == "NoBacteria"){
return [get_bounded_index(actual_pos_x + x), get_bounded_index(actual_pos_y + y)]; }
}
}
else{
for (var neigbourx = 1; neigbourx < grid.length; neigbourx++ ){
for (var neigboury = 1; neigboury < grid.length; neigboury++ ){
if (grid[get_bounded_index(actual_pos_x + neigbourx)] [get_bounded_index(actual_pos_y + neigboury)] == "NoBacteria"){
return [get_bounded_index(actual_pos_x + neigbourx), get_bounded_index(actual_pos_y + neigboury)];
}
}
}
}
}
function binomial_draws(n,p){
var number_of_success=0;
for (var i = 0; i < n; i++){
var random_number = Math.random();
if (random_number < p){
number_of_success = number_of_success+1;
}
}
return number_of_success;
}
// run all simulations
function run_simulation(){
var population_sizes = [];
population_sizes.push(N);
var time_counter =0;
// calculate the intermediate population sizes
for (var i = 0; i < time_lapse_in_minutes; i++){
time_counter = time_counter + 1;
var new_N = next_time_step(population_sizes[i]);
population_sizes.push(new_N);
update_grid(grid);
}
}
//If random positioning of the colony of N first bacteria
///////////////////////////////////////////////////////////////
// adapted from https://stackoverflow.com/questions/22648516/how-to-draw-rectangle-spiral
/*var posx = random_between(0, grid_length+1);
var posy = random_between(0, grid_length+1);
var start_posx=[];
start_posx[0]=posx;
var start_posy=[];
start_posy[0]=posy;
var width = Math.sqrt(N)+1;
var height = Math.sqrt(N)+1;
var x = -(width - height)/2;
var y = 0;
var dx = 1;
var dy = 0;
var x_limit = (width - height)/2;
var y_limit = 0;
var counter = 0;
while (counter<N){
if( dx > 0 ){//Dir right
if(x > x_limit){
dx = 0;
dy = 1;
}
}
else if( dy > 0 ){ //Dir up
if(y > y_limit){
dx = -1;
dy = 0;
}
}
else if(dx < 0){ //Dir left
if(x < (-1 * x_limit)){
dx = 0;
dy = -1;
}
}
else if(dy < 0) { //Dir down
if(y < (-1 * y_limit)){
dx = 1;
dy = 0;
x_limit += 1;
y_limit += 1;
}
}
counter += 1;
x += dx;
y += dy;
start_posx.push(start_posx[start_posx.length-1]+ dx);
start_posy.push(start_posy[start_posy.length-1]+ dy);
}
for (var i = 0; i < N; i++){
bacterium.push(new_bacterium(random_between(0, (1/division_rate)+1), start_posx[i], start_posy[i]));
}
*/
///////////////////////////////////////////////////////////////
//If random positioning of N first bacteria
init_grid();
for (var i = 0; i < N; i++){
var posx = random_between(0, grid_length+1);
var posy = random_between(0, grid_length+1);
while (grid[posx][posy] == "Bacterium") {
posx = random_between(0, grid_length+1);
posy = random_between(0, grid_length+1);
}
bacterium.push(new_bacterium(random_between(0, (1/division_rate)+1), posx, posy)); // bacteria at the beginning are not synchronized
}
init_grid();
draw_grid(grid);
//run_simulation();
function simulate_and_visualize(){
next_time_step();
update_grid(grid);
}
setInterval(simulate_and_visualize,20);
</script>
</body>
</html>
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