FloaTiles project
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Floatiles: Self-Assembly Based On Cheerios Effect and Aperiodic Monotiles
Abstract
This project aims to create a macroscopic-scale physical experiment to explore the emergence of complex behaviors using simple foundational principles. By combining the Cheerios effect, a well-observed phenomenon in fluid dynamics, with the mathematically fascinating concept of aperiodic monotiles, we seek to manifest and investigate intricate emergent patterns.
https://karegeo.github.io/floatiles/
ALIFE 2024:
Extended Abstract: https://github.com/karegeo/floatiles/blob/main/ALife_conference_2024___Submission_32___Camera_Ready.pdf
Poster: https://github.com/karegeo/floatiles/blob/main/ALIFE_2024_OIST_LaTeX_Template__OIST_Posters-1.pdf
Introduction
Purpose:
- Investigate how fundamental principles can give rise to complex emergent behaviors in physical systems.
- Offer a tangible, visual representation of theoretical concepts, making them more accessible and compelling.
Why it Matters:
Emergent phenomena are pervasive in nature, from flocking birds to economic systems. This experiment provides a controlled environment to understand the underlying principles behind such occurrences.
Latest experiments with Spectre monotile in medium container with new vibrational automatic perturbations:
Previous experiments with Hat monotile in small container with manual perturbations:
Latest experiments with Hat monotile in big container with automatic perturbations:
Previous experiments with Spectre monotile in small container:
Poster text
Cheerios Effect: Floating objects on a liquid surface come together due to surface tension and buoyancy. This phenomenon can be harnessed to control and manipulate the assembly of specific structures. The light reflection in the given figures effectively demonstrates the deformation of the water surface around the floating objects. This deformation results in the force that pulls objects together, allowing for controlled aggregation of structures.
Aperiodic Tiling: covering a whole plane without a repeating pattern using a single tile type. The 2023 discovery of the “hat” and “spectre” offers a unique geometric shape that can be incorporated into the experiment. Tiles can be created using 3D printing or laser cutting. They were introduced to a water surface to see how they aggregate based on the Cheerios Effect.
The “FloaTiles” project combines two ideas to demonstrate how individual tiles interact through the Cheerios Effect to produce emergent behavior.
The system can produce more complex patterns by adding tiles and stationary elements (engines) that have specific effects like attraction and repulsion. Patterns can affect the level of perturbation in real-time by the feedback loop of the video from the camera.
Background
The Cheerios Effect
- A phenomenon where floating objects (like cereal in milk) clump together or cling to container sides.
- Governed by three physics concepts:
- Buoyancy: Determines whether an object floats.
- Surface Tension: Causes the liquid’s surface to behave like a flexible membrane.
- Meniscus Effect: Causes the liquid to curve where it meets the container.
Aperiodic Monotiles
- Geometric shapes that, when tiled, don’t produce a repeating pattern.
- “The hat” and “Spectre” shapes are recent discoveries in this domain.
- Such tiles possess both mathematical beauty and potential for real-world applications.
Methods
Experiment Setup:
- Materials: Used 3D printers to produce buoyant objects inspired by the recent aperiodic monotile discoveries.
- Procedure: Floated the 3D-printed shapes on water surfaces.
- Observations: Watched for aggregation and the resultant unique patterns formed by these shapes under the influence of the Cheerios effect.
Observations:
- Different shapes led to varied patterns and formations.
- Vibration, either from external motors or manual input, influenced the speed and nature of the aggregation process.
Results & Analysis
- The aperiodic monotiles, when floated on water, exhibit the Cheerios effect, resulting in unique and unpredictable patterns.
- The emergent patterns observed showcased a bridge between mathematical concepts and real-world physics phenomena.
- The behavior of these tiles, especially under influence, can mimic the results of diffusion-limited aggregation simulations.
Future Implications & Applications
- Scientific Understanding: A better grasp of emergent behaviors in physical systems.
- Art & Design: Inspiration for non-repetitive patterns and designs.
- Technology: Potentially, the development of new materials or systems based on aperiodic patterns.
References
- Penrose, L. (1958). Mechanics of Self-Reproduction. Annals Of Human Genetics, 23, 59-72.
- Virgo, N., Fernando, C., Bigge, B., & Husbands, P. (2012). Evolvable Physical Self-Replicators. Artificial Life, 18, 129-142.
- Vella, D., & Mahadevan, L. (2005). The “Cheerios effect”. American Journal Of Physics, 73, 817-825.
- Smith, D., Myers, J., Kaplan, C., & Goodman-Strauss, C. (2023). An aperiodic monotile. arXiv:2303.10798.
- Smith, D., Myers, J., Kaplan, C., & Goodman-Strauss, C. (2023). A chiral aperiodic monotile. arXiv:2305.17743.
Contributing & Feedback
If you’re interested in extending this experiment or have observations of your own, please contribute to this repository or leave feedback through Issues.
Detailed Insights
The Cheerios Effect: A Deep Dive
The Cheerios effect is a commonly observed phenomenon, particularly during breakfast! At a fundamental level, this effect is an interplay of several physical forces:
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Buoyancy: Dictates if an object will float or sink. Objects less dense than the fluid will float, and those denser will sink. This principle ensures our 3D printed shapes stay afloat.
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Surface Tension: At a liquid’s surface, the molecules stick together more closely than they do to the air above, creating a sort of ‘skin’ effect. This skin can be distorted by floating objects, leading to potential attractive forces.
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Meniscus Effect: At the edges of a container, liquids tend to curve upwards or downwards. This curvature can influence the movement of floating objects, often pushing them to the edges.
Together, these forces and effects cause floating objects to attract each other and the walls of their container, resulting in clusters and clumps.
Aperiodic Monotiles: From Penrose to the Present
Aperiodic monotiles are shapes that can cover a plane without leaving gaps but in a non-repeating pattern. They are intriguing from a mathematical standpoint and have been a subject of interest for decades.
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Roger Penrose: In the 1970s, the Nobel-prize-winning physicist discovered a set of shapes (known as Penrose Tiles) that could cover a surface aperiodically. However, they worked as a set and not as individual monotiles.
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“The Hat” & “Spectre”: Recent discoveries have found individual tiles, notably the 13-sided “hat” and the curved “Spectre,” which can cover a plane without repeating patterns. These shapes brought new dimensions to the study of aperiodic tiling, bridging the gap between theory and tangible representation.
These shapes, particularly when made tangible through 3D printing, offer incredible insights into patterns, structures, and the nature of order and chaos.
Diffusion-Limited Aggregation (DLA)
DLA is a process in which particles undergo random walks due to diffusion and cluster upon contact. It’s a phenomenon observed in various systems, from the growth of coral reefs to mineral deposits. In the context of this project, the emergent patterns formed by the floating aperiodic tiles can sometimes mimic the results of DLA simulations, offering a macroscopic and controlled environment to study such phenomena.
Conclusion
The study of simple systems to derive complex behaviors has always been a cornerstone of scientific exploration. By diving deep into the nuances of these foundational principles, we are better equipped to understand, predict, and innovate in our ever-evolving world.
Contributing & Feedback
If you’re interested in extending this experiment or have observations of your own, please contribute to this repository or leave feedback through Issues.
References and aknowledgments
https://cs.uwaterloo.ca/~csk/spectre/ for dicovery
https://github.com/christianp/aperiodic-monotile for files
https://stablediffusion.fr for QR code
OIST, especially Brian Morrissey and Stephen Estelle for help with the all equipment, and to Roman Mukhin for first 3D print. Ikegami lab (UTokyo), especially Dr Ikegami and johnsmith
More links:
https://arxiv.org/abs/2301.03397 Evaporation-induced self-assembling of few-layer graphene into a fractal-like conductive macro-network with a reduction of percolation threshold
Particles of larger charge forming “molecules” by Nils Berglund @NilsBerglund