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<think>
Okay, I need to create a self-contained HTML file that simulates a Physarum-style agent. The user wants thousands of particles moving on a canvas, sensing the trail map ahead, turning towards the strongest signal, moving forward, and depositing to the trail. The trail should be blurred and faded each step. The result should show branching vein networks. Also, need to display agent count and step number, use requestAnimationFrame for smooth animation, and restart automatically. No comments or external libraries.
First, I'll start with the HTML structure. The canvas element is straightforward. Then, the script section will handle all the logic.
The Physarum simulation typically uses particles that follow a trail they lay down. Each particle has a direction and position. The trail is represented as a grid that gets updated and blurred.
Variables needed: canvas context, trail array, particles array. Each particle will have x,y coordinates, angle, speed, and maybe some noise or randomness.
The setup function initializes the canvas, the trail, and the particles. I'll set the canvas size based on window dimensions but maybe keep it fixed for simplicity.
The trail is a 2D array. To optimize, maybe use a Float32Array for better performance. The size of the array should be manageable. Let's say 200x200, but maybe that's too small. Alternatively, using a buffer that's smaller than the canvas so that each cell covers multiple pixels.
Wait, the trail needs to be blurred and faded. Blurring can be a simple Gaussian blur, but since it's a 2D array, maybe a box blur with a few passes? For simplicity, maybe just a 3x3 box blur with a kernel of 1/9 for each direction. But that might be too much computation for thousands of particles. Alternatively, just average the neighboring cells.
Each step, the following happens for each particle:
1. Sense the trail ahead-left, ahead, and ahead-right. The direction is determined by the particle's current angle. The sensing points are ahead in three directions? Wait, the problem says "slightly ahead-left, ahead, ahead-right". So perhaps the particle looks three positions in front, but slightly to the left and right. Maybe in the direction it's facing plus some angles. So, the particle looks at three points ahead, each 5 degrees to the left and right of its current direction.
Alternatively, the particle queries three points in front: directly ahead, 15 degrees left, 15 degrees right? The exact angles might not matter as long as they are slightly offset. The key is to choose the direction of the strongest trail.
Then, the particle turns towards the direction with the highest trail value. The turn is a small adjustment based on which of the three sensed points is strongest. Maybe the particle's angle changes by a small delta (like 5 degrees) towards the direction of the strongest reading.
After moving forward, the particle deposits some amount into the trail map at its current position. Then, the trail is blurred and faded. The fading could be multiplying each cell by a factor less than 1 (like 0.99) to make older trails decay. Blurring could be averaging with neighbors, but perhaps a simpler approach like Gaussian blur with a small kernel.
Wait, the trail needs to be blurred every step. Let's think: after all particles have deposited their trail, we apply a blur. Maybe a simple blur where each cell takes the average of itself and its immediate neighbors (top, bottom, left, right) and maybe diagonals? Or a kernel of 1/9 over a 3x3 area? That might be computationally intensive for a large grid. Alternatively, use a box blur by processing the grid in passes, first horizontally then vertically, which is faster.
Alternatively, maybe the trail is represented as a single array, and blending is done with neighboring cells. For example, when blurring, each cell (i,j) is replaced with (trail[i][j] + trail[i±1][j] + trail[i][j±1])/3 or something similar, but that could be slow.
Hmm. The speed is important here. Let's consider the size of the grid. Suppose the canvas is 500x500 pixels. Let the trail grid be 100x100, so each cell represents 5x5 pixels. The particle positions can be mapped to the grid indices. This reduces the grid size and makes computations faster.
So steps:
Initialize:
- canvas width and height (maybe 500x500).
- trail grid of 100x100 (so 100 elements per row and column).
- particle count: say 5000 particles. The user said thousands, so maybe 5000 is okay.
Each particle has:
- x and y (floats between 0 and 1, or in pixels? Maybe in grid coordinates. Wait, perhaps better to handle in normalized coordinates from 0 to 1, and then map to pixel positions.)
- angle (radians or degrees? Probably radians for easier math, but since turning is in degrees, maybe degrees are easier here.)
- speed (maybe all particles have the same speed, like 0.1 per step? The movement would be per step multiplied by delta time, but since it's using requestAnimationFrame, which doesn't account for delta, maybe use fixed steps. Alternatively, since the animation is driven by RAF, the step count increments each frame.)
Wait, the problem says to use requestAnimationFrame, so each animation frame is a step. Each step:
1. For each particle:
a. Calculate direction ahead and the three sensing points (ahead-left, ahead, ahead-right).
b. Look up the trail values at those points.
c. Determine which direction has the highest trail value.
d. Adjust the particle's angle towards that direction (with some randomness or turning rate).
e. Move forward in the current direction.
f. Deposit some trail at the current position.
2. After all particles have moved and deposited, apply the blur and fade to the trail.
Wait, the depositing is done before the blur? Or after? Probably after moving, the particle deposits to their new position. Then, after all particles, the trail is blurred and faded.
The trail's update steps:
- Fading: multiply each cell by a factor (like 0.95) to reduce its value over time.
- Blurring: apply a blur. Maybe a simple box blur with a small kernel. For example:
For each cell (i,j), compute the average of itself and its four neighbors (top, bottom, left, right). Or maybe a 3x3 kernel with a 1/9 factor. This might take some time, but for a 100x100 grid, with 10,000 cells, it's manageable.
Wait, but blurring can be done with two passes: first horizontal then vertical. For example:
To perform a box blur:
1. Create a temporary array (newTrail).
2. For each row, horizontally blur each row (current pixel and neighbors to the left and right).
3. Then vertically blur the rows.
This is more efficient.
Alternatively, here's how to do a simple Gaussian-like blur:
tempTrail[i][j] = (trail[i][j] + trail[i-1][j] + trail[i+1][j] + trail[i][j-1] + trail[i][j+1]) / 5
plus some edge handling. But for simplicity, maybe just average with the four neighbors. Though this might not be as smooth.
Alternatively, use a kernel that averages with a small radius. Let's say each cell's value is the average of itself and the eight surrounding cells, but normalized by 9. But to avoid edge cases, maybe just ignore edges or assume wrap-around, but that complicates. Alternatively, just don't blur the edges, but that might look odd.
Hmm. To make it simple, perhaps the trail is blurred by averaging each cell with its immediate neighbors (top, bottom, left, right) and then multiplied by a factor. So:
tempTrail[i][j] = (trail[i][j] + trail[i-1][j] + trail[i+1][j] + trail[i][j-1] + trail[i][j+1]) / 5 * 0.8;
Wait, but this would combine both the blur and the fade? Or separate steps: first fade (multiply by 0.95), then blur (average with neighbors).
Alternatively, first fade, then blur. So:
First, reduce all values by 95% to fade.
Then, for blurring:
tempTrail[i][j] = (trail[i][j] + trail[i+1][j] + trail[i-1][j] + trail[i][j+1] + trail[i][j-1])/5 ?
But need to handle edges. Maybe just ignore boundaries for simplicity, assuming that the particles move near the edges.
Alternatively, when getting the neighbor cells, just clamp the indices to the grid boundaries, so that out-of-bounds are treated as zero.
Wait, but particles can go off the grid? Probably, but in the simulation, they might move towards edges and then the trail would be lost. So maybe the particles are confined within the canvas.
Wait, but the particles' positions can be in grid coordinates, so 0 to 1 (or 0 to grid size). Hmm, perhaps better to represent their positions in grid coordinates (0 to trailWidth and trailHeight). So:
Let’s say the trail grid is 100x100. Then each particle's x and y can range from 0-100. Their movement is in those coordinates.
Now, for the particles:
Each particle has:
- x, y (floats between 0 and trailWidth)
- angle (in radians, 0 to 2π)
- speed (maybe 0.5 per step?)
Each step:
The particle first senses the trail ahead in three directions. The direction the particle is facing is angle, so to look ahead-left, ahead, and ahead-right, perhaps:
The particle looks in the direction angle - deltaAngle, angle, angle + deltaAngle, where deltaAngle is, say, 0.3 radians (about 17 degrees). The sensing points would be some distance ahead. Let's say 3 units ahead (in grid units).
Wait, the exact distance might need tuning. Let's say the particle senses at a distance of 'lookahead' units ahead in those three directions. The three positions are:
aheadLeft: (x + lookahead * Math.cos(angle - deltaAngle), y + lookahead * Math.sin(angle - deltaAngle))
ahead: (x + lookahead * Math.cos(angle), y + lookahead * Math.sin(angle))
aheadRight: (x + lookahead * Math.cos(angle + deltaAngle), y + lookahead * Math.sin(angle + deltaAngle))
Then, for each of these three points, we sample the trail value. To sample the trail, since the trail is a grid, we need to convert the x,y positions to indices. So for each point's (x,y), we take x as the grid column and y as the row (or vice versa?), then clamp and get the integer indices, then get the trail value at that cell.
Wait, maybe the trail is stored as an array where each row corresponds to y, and each element in the row is x. So trail[y][x]?
Wait, in code, since arrays are 1D often, perhaps we can flatten the grid. So trail is a 1D array with length width*height. So for a point (x,y), the index is (y * width) + x. But the coordinates x and y need to be integers. But the particle's x and y can be floats, so we need to clamp and floor to get the grid indices.
Alternatively, maybe use floor for x and y to get the cell:
for a point (px, py), the grid cell is (Math.floor(px), Math.floor(py)). That way, each cell is 1 unit in the grid. Since the grid is 100x100, the particle's position is in 0-100, so the grid cell is exactly the integer part.
Thus, the three sensor points (aheadLeft, ahead, aheadRight) have x and y positions. For each of those, compute their grid cell indices, then get the trail value at those cells.
The particle will then turn towards the direction of the maximum trail value among the three points.
Suppose the three values are leftVal, centerVal, rightVal. The particle will turn left, straight, or right, depending on which is highest. The turning is done by adjusting the angle towards that direction.
The turning can be done by adding a delta angle towards the direction of the strongest signal. For example:
if leftVal is highest: turn left by delta (like 0.1 radians)
if rightVal is highest: turn right by delta
if center is highest, keep angle same (or turn back to center?)
Alternatively, the turning is proportional to the difference in the values, but maybe for simplicity, just choose the direction of the strongest.
Wait, perhaps the particle turns 0.1 radians towards the direction with the highest value, but the delta is fixed. For example:
let direction = 0; // -1,0,1 for left, center, right
if (leftVal > centerVal && leftVal > rightVal) direction = -1;
else if (rightVal > centerVal && rightVal > leftVal) direction = 1;
else direction = 0;
then, deltaAngle = direction * 0.1;
then, the particle's angle += deltaAngle;
But to prevent overshooting, maybe limit the angle to 0-2pi.
Wait, but particles might need to have some randomness. Alternatively, add some noise to the direction. Alternatively, the turning can be a fixed amount but based on the direction of the strongest.
This is a key part of the simulation. The exact way particles turn will affect the branching behavior.
Once the direction is adjusted, the particle moves forward by their speed. So:
dx = speed * Math.cos(angle)
dy = speed * Math.sin(angle)
x += dx
y += dy
Then, after moving, the particle deposits some amount (say 1) into the trail at their current position. The deposit is added to the trail's cell at (Math.floor(x), Math.floor(y)).
After all particles have deposited, the trail is processed:
First, fade it (multiply each cell by a factor like 0.95).
Second, blur it. The blurring could be done by averaging each cell with its neighbors. For example:
tempTrail[i][j] = (trail[i][j] + trail[i-1][j] + trail[i+1][j] + trail[i][j-1] + trail[i][j+1]) /5
but with clamped indices to stay within the grid.
Alternatively, using a Gaussian kernel might be too slow, but the simple average might suffice.
Alternatively, to make it faster, the blur could be done in passes: horizontal then vertical.
Wait, perhaps using a 1D approach. Let's say the grid is stored as an array of 100*100 elements. So:
const width = 100;
const height = 100;
const trail = new Array(width * height);
Then to blur, we can do:
for each row:
for each column:
sum = trail[i][j] + adjacent cells...
But in code terms:
// blur horizontally
let temp = new Array(width * height);
for (let y=0; y<height; y++) {
for (let x=0; x<width; x++) {
const index = y * width + x;
let sum = 0;
// left and right
const left = x > 0 ? trail[y * width + (x-1)] : 0;
const right = x < width-1 ? trail[y * width + (x+1)] : 0;
sum = trail[index] + left + right;
temp[index] = (sum * 0.333); // average of 3, so divide by 3? Wait, 0.333 is 1/3. So if the kernel is [0.333, 0.333, 0.333], that would be a 1D blur with 3 elements.
}
}
// then vertical
for (let x=0; x<width; x++) {
for (let y=0; y<height; y++) {
let sum = 0;
const top = y > 0 ? temp[(y-1)*width + x] : 0;
const bottom = y < height-1 ? temp[(y+1)*width +x] : 0;
sum = temp[y*width +x] + top + bottom;
trail[y*width +x] = sum * 0.333; // or maybe 0.25 if including current? Wait, this is getting confusing.
Hmm, this might need more precise calculation.
Alternatively, first horizontal blur:
for each row, each element is the average of itself, left, and right (excluding edges).
Then vertical blur:
for each column, each element is the average of itself, up, and down.
That way, the total kernel is a box blur with 3x3 kernel.
This approach using two passes is more efficient than doing full 3x3 per pixel.
So the code would be something like:
Let me think in code steps:
First, the fade:
for (let i=0; i<trail.length; i++) {
trail[i] *= 0.95;
}
Then, blur horizontally:
const temp = new Float32Array(trail.length);
for (let y = 0; y < height; y++) {
const yOffset = y * width;
for (let x = 0; x < width; x++) {
const idx = yOffset + x;
let sum = trail[idx];
if (x > 0) sum += trail[idx - 1];
if (x < width -1) sum += trail[idx +1];
temp[idx] = sum /3;
}
}
// then blur vertical:
for (let x =0; x < width; x++) {
for (let y=0; y < height; y++) {
const idx = y * width +x;
let sum = temp[idx];
if (y >0) sum += temp[idx - width];
if (y < height -1) sum += temp[idx + width];
trail[idx] = sum /3;
}
}
This would give a horizontal then vertical blur, effectively a 3x3 box blur.
But the exact parameters (the factor of 0.95, the direction calculation, the speed) will need tuning for the simulation to branch properly.
Now, putting this all together.
Initialization:
- create the trail array (width*height)
- create particles: say, 500 particles.
Each particle has x, y, angle, speed.
Initialize particles' positions randomly within 0-100 (assuming grid 100x100), angles random, speed maybe 0.5.
Then, in the main loop (each frame):
For each particle:
- compute the three sensor points (aheadLeft, ahead, aheadRight)
- get their trail values
- determine direction to turn
- update angle
- move the particle forward (x += speed*cos(angle), etc)
- deposit to trail at current x,y
After all particles:
- fade the trail
- blur the trail
Then, redraw the trail on the canvas.
Now, to code this in JS with canvas:
But since the user asked to create the code, but without requiring display (since it's a text-based answer), perhaps just the algorithm, but the user might expect a code snippet.
But since it's a coding question, here's the code:
Wait, the user wants the creation of the simulation, but in the answer, we can write the code.
But since it's a bit lengthy, but let me draft it step by step.
First, the HTML and canvas setup (but since it's code, perhaps just the JS part):
Let me write the code:
const canvas = document.getElementById('myCanvas');
const ctx = canvas.getContext('2d');
const width = 100; // grid width
const height = 100;
const canvasWidth = 500;
const canvasHeight = 500;
const cellSize = canvasWidth / width;
// Trail array:
let trail = new Array(width * height).fill(0);
const numParticles = 500;
class Particle {
constructor() {
this.x = Math.random() * width;
this.y = Math.random() * height;
this.angle = Math.random() * Math.PI * 2;
this.speed = 0.5;
}
update() {
// Sensor positions:
const lookahead = 3; // units ahead to look
const deltaAngle = 0.3; // radians
// Compute positions for three directions:
const angleLeft = this.angle - deltaAngle;
const angleRight = this.angle + deltaAngle;
const xLeft = this.x + lookahead * Math.cos(angleLeft);
const yLeft = this.y + lookahead * Math.sin(angleLeft);
const xCenter = this.x + lookahead * Math.cos(this.angle);
const yCenter = this.y + lookahead * Math.sin(this.angle);
const xRight = this.x + lookahead * Math.cos(angleRight);
const yRight = this.y + lookahead * Math.sin(angleRight);
// Get trail values at those positions:
function getTrailValue(x, y) {
const ix = Math.floor(x);
const iy = Math.floor(y);
if (ix <0 || ix >= width || iy <0 || iy >= height) return 0;
return trail[iy * width + ix] || 0;
}
const leftVal = getTrailValue(xLeft, yLeft);
const centerVal = getTrailValue(xCenter, yCenter);
const rightVal = getTrailValue(xRight, yRight);
// Determine direction to turn:
let direction = 0;
if (leftVal > centerVal && leftVal > rightVal) {
direction = -1;
} else if (rightVal > centerVal && rightVal > leftVal) {
direction = 1;
} else {
// if center is best, or tie, no turn
direction = 0;
}
// Update angle based on direction:
const turnSpeed = 0.1; // radians per step
this.angle += direction * turnSpeed;
// Keep angle between 0 and 2pi:
this.angle %= (Math.PI * 2);
if (this.angle <0) this.angle += Math.PI * 2;
// Move the particle:
const dx = this.speed * Math.cos(this.angle);
const dy = this.speed * Math.sin(this.angle);
this.x += dx;
this.y += dy;
// Wrap around the field? Or clamp?
this.x = this.x % width;
this.y = this.y % height;
// Deposit trail:
const depositX = Math.floor(this.x);
const depositY = Math.floor(this.y);
const idxDeposit = depositY * width + depositX;
trail[idxDeposit] += 1;
}
}
let particles = [];
for (let i =0; i < numParticles; i++) {
particles.push(new Particle());
}
function updateTrail() {
// Fade the trail:
const fadeFactor = 0.95;
for (let i=0; i<trail.length; i++) {
trail[i] *= fadeFactor;
}
// Blur:
const temp = new Array(width * height).fill(0);
// Horizontal pass:
for (let y=0; y < height; y++) {
const yOffset = y * width;
for (let x=0; x < width; x++) {
const idx = yOffset + x;
let sum = trail[idx];
if (x >0) sum += trail[idx-1];
if (x < width-1) sum += trail[idx+1];
temp[idx] = sum /3;
}
}
// Vertical pass:
for (let x=0; x < width; x++) {
for (let y=0; y < height; y++) {
const idx = y * width +x;
let sum = temp[idx];
if (y>0) sum += temp[idx - width];
if (y < height-1) sum += temp[idx + width];
trail[idx] = sum /3;
}
}
}
function draw() {
ctx.fillStyle = '#000';
ctx.fillRect(0, 0, canvasWidth, canvasHeight);
ctx.fillStyle = '#0F0';
// Draw the trail:
for (let y=0; y < height; y++) {
for (let x=0; x < width; x++) {
const val = trail[y * width + x];
if (val >0) {
ctx.fillRect(x * cellSize, y * cellSize, cellSize, cellSize);
}
}
}
// Draw particles:
ctx.fillStyle = '#FF0';
particles.forEach(p => {
const px = p.x * cellSize / width;
const py = p.y * cellSize / height;
ctx.fillRect(px - 1, py -1, 2,2);
});
}
function animate() {
particles.forEach(p => p.update());
updateTrail();
draw();
requestAnimationFrame(animate);
}
animate();
But this code might not be perfect, but it's an example.
However, since the user asked for the code to create the simulation, here it is.