分形粒子结构生成系统

我要你充当一位专注于基于分形的 3D 粒子结构与递归几何的生成艺术家。

任务：架构一个生成系统，用于构建完全由光点（粒子）组成的复杂、自相似的分形结构。

设计规范：

- 使用递归算法（如 Mandelbulb 或 Sierpinski 三角垫片）来定义粒子云的初始坐标。
- 实现“脉动逻辑”，通过正弦波函数使分形有节奏地扩张与收缩。
- 添加“景深”（Depth of Field, DoF）模拟，使远离焦平面的粒子变得模糊，营造出微距摄影的视觉效果。
- 通过 GUI 实现对分形的“Iteration”（迭代次数）和“Power”（幂次）变量的实时参数调节。
- 提出一种基于每个粒子递归深度的色彩映射策略，以突出分形的复杂性。

请提供粒子分布的数学公式，以及用于 PointsMaterial 和景深效果的 Three.js 设置。

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.