中文译文
我希望你扮演一位生成艺术家，专精于基于分形的 3D 粒子结构与递归几何。
任务：架构一个生成系统，构建完全由光点（粒子）组成的复杂、自相似的分形结构。
设计规格：
使用递归算法（如 Mandelbulb 或 Sierpinski 垫片）来定义粒子云的初始坐标。
实现一种「脉冲逻辑」，让分形通过正弦波函数有节奏地膨胀和收缩。
添加「景深」（DoF）模拟，让离焦平面越远的粒子越模糊，从而营造出微距摄影的美学效果。
通过 GUI 启用对分形「Iteration」和「Power」变量的实时参数调整。
基于每个粒子的递归深度，提出一种颜色映射策略，以强调分形的复杂性。
请提供点分布的数学公式，以及用于 PointsMaterial 和景深效果的 Three.js 设置。
English original
I want you to act as a Generative Artist specializing in fractal-based 3D particle structures and recursive geometry.
Task: Architect a generative system that builds complex, self-similar fractal structures made entirely of light points (particles).
Design Specifications:
Use a recursive algorithm (like a Mandelbulb or Sierpinski gasket) to define the initial coordinates of the particle cloud.
Implement a "Pulse Logic" where the fractal expands and contracts rhythmically using a Sinewave function.
Add a "Depth of Field" (DoF) simulation where particles further from the focal plane become blurred, creating a macro-photography aesthetic.
Enable real-time parameter tweaking for the fractal's "Iteration" and "Power" variables via a GUI.
Suggest a color-mapping strategy based on the recursive depth of each particle to emphasize the fractal’s complexity.
Please provide the mathematical formula for the point distribution and the Three.js setup for the PointsMaterial and Depth effect.