Fluid simulation · qwen3.5-flash-02-23

Create a real-time fluid simulation on a full-screen canvas where dragging the mouse pushes swirling colored dye through the fluid.

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user

Create a real-time fluid simulation on a full-screen canvas where dragging the mouse pushes swirling colored dye through the fluid.

assistant

thinking

The user wants me to create a real-time fluid simulation in a single HTML file. This is a classic graphics programming task that can be achieved using:

1. A canvas element for rendering
2. JavaScript for the fluid dynamics simulation
3. CSS for styling

For a fluid simulation, I'll implement a simplified version of the Navier-Stokes equations commonly used in real-time fluid simulations. The key components are:
- Advection (moving particles along the velocity field)
- Diffusion (spreading out)
- Divergence removal (making the flow divergence-free/irrotational)
- Adding density and velocity at mouse position

I'll create a solver-based approach where:
1. The state is stored on two textures/buffers (one for current frame, one for previous)
2. Each frame we solve the physics
3. We render the result

Let me build this as a complete, self-contained HTML file with embedded CSS and JavaScript.

```html
<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Fluid Simulation</title>
    <style>
        * {
            margin: 0;
            padding: 0;
            box-sizing: border-box;
        }
        body {
            overflow: hidden;
            background: #000;
        }
        canvas {
            display: block;
        }
    </style>
</head>
<body>
    <canvas id="fluid"></canvas>
    <script>
        // Fluid simulation code here
    </script>
</body>
</html>
```

For the actual fluid simulation, I'll use a grid-based approach with:
- Velocity fields (u, v)


- Density field (for the dye)
- Color gradients based on density

I need to set up a proper grid system. I'll define constants for grid dimensions, cell size, and diffusion/dissipation parameters. For the core physics, advection is crucial - moving values along the velocity field by tracing back to where they came from. The solver also needs to handle viscosity and dissipation of both velocity and density over time.

A key constraint is maintaining incompressibility through pressure projection. This involves computing divergence, solving the Poisson equation for pressure, then subtracting the pressure gradient to make the velocity field divergence-free.

For the implementation, I'm using WebGL since it handles large grids efficiently. Starting with a smaller grid like 64×64 or 128×128 pixels works well, with each pixel representing a simulation cell storing its velocity and density values. I need to decide between a full WebGL approach and a simpler Canvas API implementation. Given the constraints around external resources, I should go with Canvas API which still produces impressive results.

Setting up the basic structure: initialize the canvas to fill the window, track mouse position and movement, and establish simulation parameters. The core functions will handle adding velocity and density at specific points when interacting with the simulation.

I'm building helper functions to work with the underlying buffer arrays - accessing X/Y coordinates through linear indexing, applying smoothing filters to blend color transitions, and setting up the main loop to continuously render updates.

Now I'm defining the fluid simulation class with configurable parameters like grid size, resolution scaling, and decay rates for both density and velocity. The class initializes canvases and buffers for tracking fluid state, then sets up the render loop with appropriate timing controls. d = Math.min(1, this.density[texID] * params.decay);
                        ctx.putImageData(imgData, x * res, y * res);
                    }
                }
            }
        }
        
        addVelocity(x, y, vx, vy) {
            const i = Math.floor(x / params.cellSize);
            const j = Math.floor(y / params.cellSize);
            if (i >= 0 && i < this.sizeX && j >= 0 && j < this.sizeY) {
                const idx = i + j * this.sizeX;
                this.velocities[idx] += vx * params.velDiffuse;
                this.velocities[idx + 1] += vy * params.velDiffuse;
            }
        }
        
        showDensity() {
            for (let i = 0; i < this.sizeX * this.sizeY; i++) {
                const dens = this.densities[i];
                const alpha = Math.sqrt(dens);
                this.ctx.fillStyle = `rgba(0, ${alpha * 255}, 255, ${alpha})`;
                this.ctx.fillRect(i % this.sizeX, Math.floor(i / this.sizeY), 1, 1);
            }
        }
    }

This sets up the core fluid dynamics simulation with density tracking, velocity propagation, and visual output through the canvas context.

The main initialization creates the fluid instance, applies a blue gradient tint, and binds event handlers for mouse input. When clicking or dragging, the code detects the current button state and tracks movement direction to feed velocity into the simulation at the mouse position. The animation loop repeatedly clears the canvas, renders the fluid state, adds injected velocities from mouse interaction, then requests the next frame.

I realize there's an issue with this approach—it doesn't actually implement real fluid dynamics. Let me step back and write something more authentic. I'll focus on creating a genuine fluid simulation instead.

→ write /tmp/ws/index.html (20774 bytes)

→ bash {"command":"ls -la /tmp/ws/index.html"}

toolResult

Successfully wrote 20774 bytes to /tmp/ws/index.html

toolResult

ls: cannot access '/tmp/ws/index.html': No such file or directory Command exited with code 2

assistant

thinking

The write command seems to have failed or the file was created somewhere else. Let me check what's in /tmp/ws and try writing again.

→ bash {"command":"ls -la /tmp/ws/ && pwd"}

toolResult

total 24 drwxr-sr-x. 2 node node 24 Aug 1 17:43 . drwxrwsrwx. 3 root node 16 Aug 1 17:42 .. -rw-r--r--. 1 node node 20774 Aug 1 17:43 index.html /tmp/ws

assistant

thinking

The file was successfully created. The `ls -la` command confirms the file exists at `/tmp/ws/index.html` with 20774 bytes.

I've created a complete real-time fluid simulation in a single self-contained HTML file. Here's what it does:

**Features:**
- **Real-time Navier-Stokes solver** - Uses semi-Lagrangian advection and projection methods to simulate fluid physics
- **Mouse interaction** - Dragging the mouse pushes the fluid (causing swirling motion) and adds colored dye
- **Touch support** - Works on mobile devices as well
- **Rainbow color effects** - Colors shift over time with smooth HSL-based coloring
- **Full-screen canvas** - Auto-resizes to fit any viewport

**How to use:**
1. Open the file in a web browser (`/tmp/ws/index.html`)
2. Click and drag your mouse across the screen to push swirling colored dye through the fluid
3. Watch the dye swirl, mix, and gradually dissipate

The simulation runs entirely client-side with no external dependencies or network requests.

TAKE IT TO CODE

A single self-contained HTML file — copy it and open in any browser, or reuse the prompt with your own pi-agent run.

RUN

modelqwen3.5-flash-02-23

vendorQwen

harnesspi-agent

generated2026-08-01

EVALUATION

★★★★★ 3/5 partial

Fluid sim reacts strongly to dragging with colored dye, but idle screen is blank black and other inputs show only a lingering static gradient.

Vision grade · anthropic/claude-sonnet-5

MEASUREMENTS

Raw readings from the capture, not a verdict — the grade above is the only judgement. Percentages are how much of the screen changed; the measure under-reports sparse motion on a dark background.

idle motion0.0%

on click0.0%

on drag99.4%

on wheel0.0%

on arrow keys0.0%

on w/a/s/d0.0%

frame spread17.9 / 255

console errors0

js errors none

METRICS

runtime43.7s

tokens in15k

tokens out6.7k

cached0

cost / run$0.0027