In high school we used Newton's method to solve polynomials. Then we got an equation and just a slight change in the starting point gave a different solution.

In high school we used Newton's method to solve polynomials. Then we got an equation and just a slight change in the starting point gave a different solution. We started plotting everything on graph paper. Then we wrote a program in MathCAD to calculate the numbers for us and plot it. Then we wrote a program to plot the solutions. Then we added color to the program. It was then that our teacher told us that we had created a fractal. We then played around with fractint, learned about some real world cases of fractals, a little about chaos theory and weather prediction. I loved it all. The best part was rather than our teacher just saying "here is a fractal" we "discovered" it on our own each day over the course of a week. https://en.wikipedia.org/wiki/Newton_fractal https://en.wikipedia.org/wiki/Newton_fractal https://www.fractint.org/ https://www.fractint.org/