A Visual Narrative of Our Project's Progress
The animations presented here were carefully crafted to showcase a selection of the progress made in our project. We are delighted to offer the source code for all the animations as a complimentary resource, easily accessible by clicking on the </> icon located in the upper right corner. These animations have been created utilizing the versatile JavaScript library, P5.js, and some have been designed to provide an interactive experience, allowing users to engage with the animation by interacting with its various elements. For further code samples, please visit our GitHub account.
The Active Elastic Model is a minimal model for self-propelled agents that interact through attraction, repulsion, and alignment using elastic interactions. It has a simple mechanical realization and can be applied to real-world systems such as active cell membranes and robotic or animal groups. The agents are connected to their neighbors by linear springs located a certain distance R in front of their centers of rotation. Depending on the value of R, the elastic interactions mainly produce attraction-repulsion or alignment forces.
This animation illustrates the alignment process in the Active Elastic Model. It depicts three agents connected by springs. The radius R is represented in black, while the springs are colored blue and red. When the distance between agents exceeds the natural length of the spring, the connecting line is blue, and red when the distance is less. The agents' alignment force, determined by the agents' distance and the radius R, is illustrated in green. The animation also demonstrates how the alignment of the agents shifts as one agent randomly moves, due to the forces exerted by the springs. You can interact with the other two agents by dragging them on the screen to choose a new position.
Force-directed graph drawing is an algorithm for visualizing complex network structures, such as social networks, transportation networks, or biological networks. The algorithm uses a physical metaphor, where nodes in the network are treated as particles and edges as springs, and simulates the forces acting on the particles using physical principles such as Hooke's law. The goal of the algorithm is to minimize the energy of the system, which results in a layout that is easy to read and interpret.
Force-directed graph drawing is useful in network science because it can help researchers to uncover hidden patterns and relationships in large and complex networks. For example, it can be used to identify groups of highly connected nodes (called "communities" or "clusters") within a network, to reveal the structure of network hierarchies, or to identify key players or influential nodes. Additionally, force-directed graph drawing can be used to visualize relationships between nodes in a way that is easy to interpret by non-experts.
The Active Elastic Model is a simplified framework for modeling self-propelled agents that interact with one another through a combination of attraction, repulsion, and alignment forces created by elastic interactions. With a simple mechanical implementation, this model can be applied to a wide range of real-world systems, such as active cell membranes and groups of robots or animals. The agents in the model are connected to their neighbors via linear springs placed at a fixed distance, R, in front of their centers of rotation. The value of R determines the dominant force produced by the elastic interactions, either attraction-repulsion or alignment.
This animation demonstrates how agents move interactively. Users can see the equations that control the movement at the bottom of the animation. They can also adjust the parameters of these equations, as well as limit movement in specific axes. Additionally, users can manipulate the position of individual agents by dragging them. This animation not only helps explain the model, but also sparked new ideas for our research.
The Vicsek model is a mathematical model used to simulate the dynamics of particle systems that move cohesively. This model is applied in the study of living systems to understand how cells or bacteria move in a population and how they interact with each other.
In the Vicsek model, each particle has a position and a direction of movement in a two or three dimensional space. The particles move at a constant speed in the direction they are facing, and their direction of movement is randomly changed with a certain probability. In addition, the particles have a social interaction and tend to move in the same direction as their nearby neighbors.
This model allows us to predict how populations of cells or bacteria behave in a given environment. For example, it can be used to study the formation of bacterial colonies or the aggregation of cells in tissue. It can also be used to investigate how particles are organized into coherent patterns in a population, such as the formation of schools of fish.
A Boolean Network is a model that shows how different components in a system interact with each other. It only uses two values, true or false, and each component is represented by a node. The connections between components are shown as edges.
Boolean Networks are helpful in understanding how living systems work and how they can be changed to achieve specific goals.
Attractors in Boolean Networks are patterns of activity that the network can reach. These patterns can represent different states or behaviors of a living system.
In this animation, squares are used to show the state of each node in a Boolean Network. Black squares mean the node is off and white squares mean the node is on. The animation starts with a random starting point and shows how the system changes over time. After a short period, the system reaches a stable pattern, known as an attractor. The system will stay in this pattern until something changes it.
Our work on Multiscale Organizational Principles in Active Matter and Living Systems is ongoing and we will continue to update the content of this page as it progresses.
Over the course of the first year, we have made significant progress by developing a number of mathematical models to study living systems and active matter. In the near future, we will be adding further information and insights gained from our research efforts. In addition, we plan to use our models to explore the behavior of active matter and living systems at different scales.