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This paper examines a family of designs for magnetic cubes and counts how many configurations are possible for each design as a function of the number of modules. Magnetic modular cubes are cubes with magnets arranged on their faces. The magnets are positioned so that each face has either magnetic south or north pole outward. Moreover, we require that the net magnetic moment of the cube passes through the center of opposing faces. These magnetic arrangements enable coupling when cube faces with opposite polarity are brought in close proximity and enable moving the cubes by controlling the orientation of a global magnetic field. This paper investigates the 2D and 3D shapes that can be constructed by magnetic modular cubes, and describes all possible magnet arrangements that obey these rules. We select ten magnetic arrangements and assign a "color" to each of them for ease of visualization and reference. We provide a method to enumerate the number of unique polyominoes and polycubes that can be constructed from a given set of colored cubes. We use this method to enumerate all arrangements for up to 20 modules in 2D and 16 modules in 3D. We provide a motion planner for 2D assembly and through simulations compare which arrangements require fewer movements to generate and which arrangements are more common. Hardware demonstrations explore the self-assembly and disassembly of these modules in 2D and 3D.
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Modular Hardware Design with Timeline Types
Modular design is a key challenge for enabling large-scale reuse of hardware modules. Unlike software, however, hardware designs correspond to physical circuits and inherit constraints from them. Timing constraints—which cycle a signal arrives, when an input is read—and structural constraints—how often a multiplier accepts new inputs—are fundamental to hardware interfaces. Existing hardware design languages do not provide a way to encode these constraints; a user must read documentation, build scripts, or in the worst case, a module’s implementation to understand how to use it. We present Filament, a language for modular hardware design that supports the specification and enforcement of timing and structural constraints for statically scheduled pipelines. Filament usestimeline types, which describe the intervals of clock-cycle time when a given signal is available or required. Filament enablessafe compositionof hardware modules, ensures that the resulting designs are correctly pipelined, and predictably lowers them to efficient hardware.
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- PAR ID:
- 10603057
- Publisher / Repository:
- Association for Computing Machinery (ACM)
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 7
- Issue:
- PLDI
- ISSN:
- 2475-1421
- Format(s):
- Medium: X Size: p. 343-367
- Size(s):
- p. 343-367
- Sponsoring Org:
- National Science Foundation
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