The Logistics Equation There is an equation that can literally represent almost everything that happens in our world. Growth of animal populations, water dripping from a faucet, the Mandelbrot set, and much more! It is, the Logistics equation. It is a recursive function, meaning you plug in the output of the function into the function over and over again. This gives multiple outputs each based off of the output before it. The Equation is: x = rx(1-x) X is the output (And the Input in this equation) R is the growth rate (How much it grows) The reason the Population amount slowly dies down in some cases it maybe because the population ran out of food or something, so you can see this equation can represent a population growth in a controlled environment. Note: This equation only REPRESENTS different things, it won't give the real output but it may be proportional. When you increase the growth rate, as you approach value 4, the graph will seem quite chaotic. This is not actually a bug or a glitch, but is part of the equation. This is seen in nature, when a population is unsteady. This actually happens to represent a lot of things that may seem random in the world, but actually follow pretty closely to this equation. A lot of chaotic values don't follow this equation, though. If you set the growth rate to something steady, like around 2, you will see the population will always find a resting point around a certain value even if you change the Initial X value! Ask any questions about this equation in the comments. I would love to answer them :)
