A Single Equation that Rules the World
The equation connects neuron firing, fluid convection, the Mandelbrot set and so much more and will definitely change your view of this world.
What if I say that the Mandelbrot set, a population of squirrels, a dripping faucet, the firing of neurons in our brain and the thermal convection is connected by one simple equation? Maybe you’ll laugh at me. But math is stranger than fiction.
Let’s dive deep into this.
Suppose you want to model a population of squirrels. This year, we have X number of squirrels. So, what might be the population next year? A simple model can be, just multiply the current population with a number. Let it be r. so, the growth rate is r. So, next year, the number of squirrels will be rX.
If r=2, it will mean that the population will double every year. But there is a problem. It implies that the population of squirrels will grow exponentially, forever. That doesn’t really happen. So, we bound it by some constrains. Let’s add the term (1-X) to the equation to represent the constraints of the environment.
So, it becomes rX(1-X). Here we are imagining X is a percentage of the theoretical maximum. X goes from 0 to 1 and as it approaches 1, (1-X) approaches 0.
