This paper considers the shape formation problem within the 3D hybrid model, where a single agent with a strictly limited viewing range and the computational capacity of a deterministic finite automaton manipulates passive tiles through pick-up, movement, and placement actions. The goal is to reconfigure a set of tiles into a specific shape termed an icicle. The icicle, identified as a dense, hole-free structure, is strategically chosen to function as an intermediate shape for more intricate shape formation tasks. It is designed for easy exploration by a finite state agent, enabling the identification of tiles that can be lifted without breaking connectivity. Compared to the line shape, the icicle presents distinct advantages, including a reduced diameter and the presence of multiple removable tiles. We propose an algorithm that transforms an arbitrary initially connected tile structure into an icicle in $\mathcal{O}(n^3)$ steps, matching the runtime of the line formation algorithm from prior work. Our theoretical contribution is accompanied by an extensive experimental analysis, indicating that our algorithm decreases the diameter of tile structures on average.

翻译：本文研究了三维混合模型中的形状形成问题，其中具有严格受限视野范围和确定性有限自动机计算能力的单个智能体通过拾取、移动和放置操作操纵被动瓦片。目标是重新配置一组瓦片，形成称为冰锥的特定形状。冰锥被识别为致密、无孔的结构，被战略性地选择作为更复杂形状形成任务的中间形状。它设计为便于有限状态智能体探索，使其能够识别可在不破坏连通性的情况下被抬起的瓦片。与直线形状相比，冰锥具有显著优势，包括更小的直径和多个可移除瓦片的存在。我们提出了一种算法，将任意初始连接的瓦片结构转化为冰锥，所需步数为$\mathcal{O}(n^3)$，与先前工作中直线形成算法的运行时间相匹配。我们的理论贡献附带了广泛的实验分析，表明我们的算法平均降低了瓦片结构的直径。