Fractal Wake Field Simulation

\n\n \n \n\n\n\nThis creates a basic Three.js scene with a rotating cube, which we can replace with more complex fractal geometry later.\n\n2. Shader Code for 3D Fractals:\n\nNow let's focus on the GLSL shader code. We'll need to write both a vertex shader and a fragment shader to handle the fractal and wake field interaction.\n\nFragment Shader (GLSL):\n\nHere’s an example fragment shader that might simulate a 3D Mandelbrot fractal in the context of a wake field. The wake field can be simulated using noise functions that influence the fractal generation.\n\nprecision highp float;\n\nuniform float time;\nuniform vec3 cameraPosition;\nuniform vec3 wakeFieldStrength;\n\nvarying vec3 vPosition;\n\nfloat mandelbrot(vec3 p) {\n float maxIter = 100.0;\n float escapeRadius = 2.0;\n vec3 c = p;\n for (float i = 0.0; i < maxIter; i++) {\n p = vec3(p.x * p.x - p.y * p.y - p.z * p.z + c.x,\n 2.0 * p.x * p.y + c.y,\n 2.0 * p.x * p.z + c.z);\n if (length(p) > escapeRadius) {\n return i / maxIter;\n }\n }\n return 0.0;\n}\n\nfloat noise(vec3 p) {\n return fract(sin(dot(p, vec3(12.9898, 78.233, 54.53))) * 43758.5453);\n}\n\nvoid main() {\n // Compute fractal position, influenced by wake field\n vec3 p = vPosition * 0.5 + cameraPosition;\n p += wakeFieldStrength * sin(time * p.x * p.y); // Wake field influence\n float fractalValue = mandelbrot(p);\n\n // Use the fractal value and noise to influence the color\n vec3 color = vec3(fractalValue) * noise(p * 0.1);\n gl_FragColor = vec4(color, 1.0);\n}\n\nBreakdown:\n\nMandelbrot Function: This function calculates the fractal pattern by iterating over a point in 3D space. It returns a value representing how quickly the point \"escapes\" the fractal boundary, which is then mapped to color.\n\nNoise Function: The noise is used to simulate the wake field in the fractal space, affecting its generation. It can be modified to create more complex field interactions.\n\nWake Field Influence: The wakeFieldStrength uniform is used to modify the fractal generation formula in a way that changes the fractal pattern over time, simulating the effects of the wake field.\n\n\n3. Vertex Shader (GLSL):\n\nThe vertex shader processes the geometry. For this example, you can start with something basic for rendering a 3D object:\n\nprecision highp float;\n\nattribute vec3 position;\nuniform mat4 modelViewMatrix;\nuniform mat4 projectionMatrix;\nvarying vec3 vPosition;\n\nvoid main() {\n vPosition = position;\n gl_Position = projectionMatrix * modelViewMatrix * vec4(position, 1.0);\n}\n\nThis passes the 3D position of each vertex to the fragment shader for further processing.\n\n4. JavaScript Logic:\n\nIn JavaScript, we would update the wake field strength and time uniforms to animate the fractal over time. Here's how you might set that up:\n\nconst material = new THREE.ShaderMaterial({\n vertexShader: `/* vertex shader code goes here */`,\n fragmentShader: `/* fragment shader code goes here */`,\n uniforms: {\n time: { type: 'f', value: 0 },\n wakeFieldStrength: { type: 'v3', value: new THREE.Vector3(0.1, 0.1, 0.1) },\n cameraPosition: { type: 'v3', value: camera.position }\n }\n});\n\nfunction animate() {\n requestAnimationFrame(animate);\n material.uniforms.time.value += 0.01;\n renderer.render(scene, camera);\n}\n\nanimate();\n\nHere, the wakeFieldStrength can be manipulated to simulate changes in the external field as time progresses, affecting the fractal's growth. The time uniform allows the wake field to evolve dynamically.\n\nFinal Notes:\n\n3D Fractal Representation: You could extend this basic framework by using more complex 3D fractal algorithms, like the Mandelbulb or Julia sets in 3D, for more intricate patterns.\n\nWake Field Simulation: More advanced simulations of wave propagation could be included by applying Perlin noise or simplex noise to simulate the field’s influence more realistically, especially as it interacts with fractal growth.\n\nOptimizations: Depending on the complexity of the fractals and the number of calculations per pixel, you might want to optimize the shader for performance, especially when handling recursive calculations.\n\n\nThis provides a basic framework for generating 3D fractals with a wake field influence using WebGL and three.js. The generalized Hausdorff dimension could be indirectly approximated through the fractal generation process, especially if you use recursive formulas and dynamically scale the fractal’s iterations based on field influences.\n","url","link_url","/p/tqpu3abffglo5fknvs2i","versioned_link_url","/p/tqpu3abffglo5fknvs2i/1","yapping","cursor","eyJpZCI6InRxcHUzYWJmZmdsbzVma252czJpIn0","token","included",[],"routes/browser/layout","actionData","errors"]

3D Fractal Wake Field Simulation