Set the 'seed' value of x at the slider. Click on the green flag and observe what value Scratch the cat says x is attracted to. The concept of an 'attractor' is crucial to chaos theory. The Lorenz attractor is just one example of the many attractors studied in a chaos course. Math students easily recognize the function in the machine as a 'linear' function of the form y = mx +b. It's linear because it graphs as a straight line. But, in this project, the function isn't 'graphed', it's iterated, and its behavior is quite different. A starting value, called the 'seed', is given to the function but from there on, at every iteration, the output value of x becomes the new input value of x. Instead of a line, the function, when iterated, is a series of points that are 'attracted' to a number.
This is a simple algebraic attractor I give students early in a first course on chaos theory. In the course, we spend a lot of time on the distinction between graphing a function and iterating a function. The concept of iteration doesn't appear in the US high school math standards. The iteration concept, along with the recursion concept, is met early in a programmer's training. See my Lorenz, Rossler, and Hennon attractor Scratch projects.
