3D Fractal with WebGL

\n \n\n\n\n\n2. Setting Up WebGL Context:\n\nIn script.js, initialize WebGL and create a rendering loop:\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\n3. Generating the Julia Set:\n\nYou can generate a 3D Julia set by iterating over a grid of complex numbers. The following function computes the Julia set values:\n\nfunction generateJuliaSet(size, c) {\n const data = new Float32Array(size * size * size);\n const maxIterations = 100;\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 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;\n zx = tmp;\n i++;\n }\n\n data[x + y * size + z * size * size] = i / maxIterations; // Normalize\n }\n }\n }\n return data;\n}\n\n\n4. Applying Convolution:\n\nYou can create a convolution kernel and apply it to the generated Julia set data. For simplicity, we can use a Gaussian blur kernel:\n\nfunction convolution(data, size, kernel) {\n const output = new Float32Array(data.length);\n const kernelSize = Math.sqrt(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)];\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 Gaussian kernel\nconst gaussianKernel = [\n 1/16, 1/8, 1/16,\n 1/8, 1/4, 1/8,\n 1/16, 1/8, 1/16,\n];\n\n\n5. Simulating Stochastic Gradient Descent with Particles:\n\nCreate a particle system that moves according to the convolved Julia set values:\n\nclass Particle {\n constructor(position) {\n this.position = position;\n this.velocity = [Math.random(), Math.random(), Math.random()];\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 this.velocity[0] += (Math.random() - 0.5) * 0.01 + force;\n this.velocity[1] += (Math.random() - 0.5) * 0.01 + force;\n this.velocity[2] += (Math.random() - 0.5) * 0.01 + force;\n this.position[0] += this.velocity[0];\n this.position[1] += this.velocity[1];\n this.position[2] += this.velocity[2];\n }\n}\n\nconst particles = [];\nfor (let i = 0; i < 1000; i++) {\n particles.push(new Particle([Math.random() * size, Math.random() * size, Math.random() * size]));\n}\n\n\n6. Rendering the Particles:\n\nFinally, render the particles based on their positions in the convolved Julia set. You may use points or spheres to represent particles:\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 // Convert particle position to screen coordinates and draw\n // ... (implement WebGL drawing code here)\n });\n\n requestAnimationFrame(render);\n}\n\nrender();\n\n\n\nConclusion\n\nThis code provides a foundational approach to generating a 3D fractal-like structure using WebGL that combines the properties of a convolved Julia set with a particle system influenced by stochastic gradient descent.\n\nThe rendering and drawing of particles would require further development in terms of shaders and buffers to visualize the particles properly. Additionally, enhancing the interaction and visual appearance can lead to even more fascinating outcomes as particles dynamically navigate through the fractal landscape influenced by the Julia set's complexity.\n\nFine-tuning parameters like the kernel for convolution, the dynamics of the particle system, and the visualization techniques will yield richer, more intricate fractal structures.","url","link_url","/p/p5202tpchyr57rzj9xj9","versioned_link_url","/p/p5202tpchyr57rzj9xj9/1","yapping","page_description","This page features a graphical display of 3D particles generated using WebGL, showcasing a fractal effect influenced by Julia set parameters. It includes…","cursor","eyJpZCI6InA1MjAydHBjaHlyNTdyemo5eGo5In0","token","included",[],"about",{"_168":-5},"parent","routes/browser/layout","actionData","errors"]

3D WebGL Fractal Particles