Strange Attractors

I wrote this program in January of 7th grade.

I became interested in Chaos theory after reading a book on the subject. It described how a scientist working on weather models liked to experiment with various equations and run them on his computer, eventually finding a really nice looking shape with some really interesting properties. I found this pretty interesting, and when the actually showed me the formulas used to make this, I felt like I should chalenge myself and figure out how to work with these.

So now in 7th grade, years away from formally learning integration, I gave myself the task of trying to figure this out. So I aproached a teacher in the highschool, and when I showed him the formulas from the book, he told me they couldnt be solved. Which was true, they couldnt be explictily solved, but I wanted to figure out what Lorenz had done and get it to work. So I asked arround a little further, and I learned that dx/dt describes the change of x over the change in time. (I learned this written with the Greek letter Δ instead of ‘d’, so thats what I ended up using in my programs). I also learned that I could multiply both sides of each of the three equations by Δt, and got me into a good state to tinker arround with my program. It took me a long time to figure out what a good value for Δt should be, and I was very happy when my program was able to plot a nice visual of the attractor in less than an hour (which is what happened before I increased Δt by a few OoM).

Here is a visual of the Lorenz attractor I made

After this project I had this nagging feeling that I really didnt get what it meant for a set of such equations to be “explicitly solvable”. To try and fix this, I wrote a number of smaller programs in which I tryed to plot different equations and got a circle to be plotted using ODEs.