Hey! You might be wondering what's going on here. Lenia is a continuous version of Conway's Game of Life, meaning the cells take on a values between 0 and 1 and space and time are defined on an infinitely small grid. Just like GoL, each cell looks at its neighbors and decides whether to increase or decrease using a function called the growth function. To make the math nice, we model this with a partial differential equation for the state of the system \(A(\mathbf{x}, t)\): \[ \frac{\partial}{\partial t} A(\mathbf{x}, t) = T(K(\mathbf{x}) * A(\mathbf{x}, t)) - A(\mathbf{x}, t) \] Where \(K*A\) is a convolution and \(T\) a is a gaussian "growth function". That's it! The purpose of this demo is to show the complex dynamic patterns that emerge on their own. After a few minutes of playing around with the canvas, you should be able to make some interesting patterns!

Instructions:

• Click and drag to draw on the canvas (you can draw while it's running!)
• Press [space] to play/pause the simulation
• Use the sliders to adjust the parameters (these change the behavior very drastically!)
• Change the shape and size of the brush and use white to erase.
• Clear the canvas to start fresh