parametric visualizer

Instructions

~WIGGLY MATH SHAPES, CLICK TO RANDOMIZE!~ These squiggles are made by what mathematicians call #parametric equations. Change the #parameters [a] and [b] to change the shape! We can call these squiggles #parametric #systems, or #parametrizations. Each system is a map of points generated using Scratch's pen tool and the equations in the top left/right corners. In this case, the system plots 1,000 (x,y) coordinates with respect to [t]. Each instance of [t] from 1 to 1,000 fills in the rest of the map. How many parametrizations exist in this project? With ten states per parameter, and four independent parameters, we get a whopping 10^4 or 10,000 possible combinations. If you adjust the slider range, you can make even more possibilities! What makes the system wiggly? In this #visualizer, each #parameter [a] and [b] is slightly adjusted over time. How slightly? So slightly that any change to [a] or [b] over 0.1% will throw the system into chaos! In parametric systems, tiny fluctuations can create huge changes in behavior. That's why these systems are sometimes also called #dynamic or #chaotic systems. Want to learn more? Leave a comment below, or see inside for code and more explanations. Feel free to REMIX with your own parametric equations! _B)_