3D Fractal with WebGL

\n \n\n\n\nIn script.js, set up the WebGL context and shaders:\n\nconst canvas = document.getElementById('canvas');\nconst gl = canvas.getContext('webgl');\n\ncanvas.width = window.innerWidth;\ncanvas.height = window.innerHeight;\n\ngl.viewport(0, 0, gl.canvas.width, gl.canvas.height);\ngl.clearColor(0, 0, 0, 1);\ngl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);\n\n// Shader setup\nconst vertexShaderSource = `...`; // Vertex shader code\nconst fragmentShaderSource = `...`; // Fragment shader code\n\nVertex Shader Example:\n\nattribute vec3 position;\nuniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nvarying vec3 vPosition;\n\nvoid main() {\n gl_Position = projectionMatrix * modelViewMatrix * vec4(position, 1.0);\n vPosition = position;\n}\n\nFragment Shader Example:\n\nprecision mediump float;\nvarying vec3 vPosition;\n\nvoid main() {\n gl_FragColor = vec4(vPosition * 0.5 + 0.5, 1.0); // Simple color mapping\n}\n\n2. Generating the 3D Julia Set\n\nTo create a more complex Julia set, enhance the iteration logic to include additional parameters. This iteration can generate richer fractal structures.\n\nfunction generateJuliaSet(size, c, maxIterations = 100) {\n const data = new Float32Array(size * size * size);\n for (let x = 0; x < size; x++) {\n for (let y = 0; y < size; y++) {\n for (let z = 0; z < size; z++) {\n let zx = 1.5 * (x / size - 0.5);\n let zy = 1.5 * (y / size - 0.5);\n let zz = 1.5 * (z / size - 0.5);\n let i = 0;\n\n while (zx * zx + zy * zy + zz * zz < 4 && i < maxIterations) {\n const tmp = zx * zx - zy * zy - zz * zz + c.x;\n zy = 2 * zx * zy + c.y;\n zz = 2 * zx * zz + c.z; // Adjust for complex behavior\n zx = tmp;\n i++;\n }\n data[x + y * size + z * size * size] = i / maxIterations; // Normalize\n }\n }\n }\n return data;\n}\n\n3. Applying Advanced Convolution Techniques\n\nInstead of a simple Gaussian kernel, consider implementing a more sophisticated kernel for convolution, such as a Laplacian or Sobel filter, to enhance edge detection and add detail.\n\nfunction convolution(data, size, kernel) {\n const output = new Float32Array(data.length);\n const kernelSize = Math.cbrt(kernel.length);\n const halfKernel = Math.floor(kernelSize / 2);\n \n for (let x = 0; x < size; x++) {\n for (let y = 0; y < size; y++) {\n for (let z = 0; z < size; z++) {\n let sum = 0;\n let weight = 0;\n\n for (let kx = -halfKernel; kx <= halfKernel; kx++) {\n for (let ky = -halfKernel; ky <= halfKernel; ky++) {\n for (let kz = -halfKernel; kz <= halfKernel; kz++) {\n const nx = x + kx;\n const ny = y + ky;\n const nz = z + kz;\n\n if (nx >= 0 && nx < size && ny >= 0 && ny < size && nz >= 0 && nz < size) {\n const index = nx + ny * size + nz * size * size;\n const kernelValue = kernel[(kx + halfKernel) * kernelSize + (ky + halfKernel) * kernelSize + (kz + halfKernel)];\n sum += data[index] * kernelValue;\n weight += kernelValue;\n }\n }\n }\n }\n output[x + y * size + z * size * size] = sum / weight; // Normalize by weight\n }\n }\n }\n return output;\n}\n\n// Example Laplacian kernel\nconst laplacianKernel = [\n 0, -1, 0,\n -1, 4, -1,\n 0, -1, 0\n];\n\n4. Implementing a Complex Particle System\n\nTo create a more dynamic particle system influenced by the convolved Julia set, adapt particles' behaviors and interactions. Introduce environmental factors, attractors, or repellers based on the fractal data.\n\nclass Particle {\n constructor(position) {\n this.position = position;\n this.velocity = [Math.random() * 0.01, Math.random() * 0.01, Math.random() * 0.01];\n }\n\n update(data, size) {\n const index = Math.floor(this.position[0]) + Math.floor(this.position[1]) * size + Math.floor(this.position[2]) * size * size;\n const force = data[index] || 0;\n\n // Introduce attraction/repulsion based on convolved data\n this.velocity[0] += (Math.random() - 0.5) * 0.01 + force * 0.1;\n this.velocity[1] += (Math.random() - 0.5) * 0.01 + force * 0.1;\n this.velocity[2] += (Math.random() - 0.5) * 0.01 + force * 0.1;\n\n this.position[0] += this.velocity[0];\n this.position[1] += this.velocity[1];\n this.position[2] += this.velocity[2];\n }\n}\n\n// Initialize particles\nconst particles = [];\nfor (let i = 0; i < 2000; i++) {\n particles.push(new Particle([Math.random() * size, Math.random() * size, Math.random() * size]));\n}\n\n5. Enhanced Rendering with Lighting and Depth\n\nTo achieve more visually compelling results, implement depth and lighting in the fragment shader, allowing for a more realistic rendering of the fractal structure and particles.\n\nFragment Shader with Lighting:\n\nprecision mediump float;\nvarying vec3 vPosition;\n\nvoid main() {\n vec3 lightDirection = normalize(vec3(1.0, 1.0, 1.0));\n float brightness = max(dot(vPosition, lightDirection), 0.0);\n gl_FragColor = vec4(brightness * vPosition * 0.5 + 0.5, 1.0);\n}\n\nFinal Rendering Loop\n\nIncorporate all parts into the main rendering loop, ensuring to clear buffers, update particles, and draw them based on their positions influenced by the convolved Julia set.\n\nfunction render() {\n gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);\n \n particles.forEach(particle => {\n particle.update(convolvedData, size);\n // Implement WebGL drawing code to represent the particle\n // For example, using point sprites or small spheres\n });\n\n requestAnimationFrame(render);\n}\n\nrender();\n\nConclusion\n\nThis revised approach enhances the complexity and intricacy of generating a 3D fractal-like structure influenced by stochastic gradient descent using a convolved Julia set. By employing advanced convolution techniques, a dynamic particle system, and improved rendering methods, the exploration of fractal structures can yield richer visual and experiential outcomes. The interplay of these elements may evoke the layered, chaotic nature of the inquiry itself, creating a visual metaphor for the complexity and absurdity inherent in existence.","url","link_url","/p/12eaq49joiz3gd_q2xza","versioned_link_url","/p/12eaq49joiz3gd_q2xza/1","yapping","page_description","The page features a 3D visualization of a Julia Set Fractal Particle System using WebGL. It includes a full-screen canvas where colorful fractal…","cursor","eyJpZCI6IjEyZWFxNDlqb2l6M2dkX3EyeHphIn0","token","included",[],"routes/browser/layout","actionData","errors"]

3D WebGL Fractal Particle System