Math
Welcome to the math page. This page contains all my math projects on the site with thier basic over head and how they came to be.
My love for math started as an elementary schooler solving large math problems in the margin of my math assignments for fun. Math was an easy and fun puzzle that never ended. You can always make a new problem to solve and there's always more rules and patterns to discover.
Last year I finished my second year of calculus (calculus II / multivariable calculus) as a junior in high school. I constantly find myself asking questions trying to find uses for the math I am learning. With my recent ability to code fairly well in java script, I have been able to expand my mathematical puzzles to new limits, employing the uses of brute force calculations and fancy operations that would be hard for a normal calculator.
Mandelbrot Set
This project was a one up to my Sierpiński triangle. I literally said "so if I can make one fractal, maybe I can make the coolest fractal..." So yeah. For those that don't know the Mandelbrot Set is a fractal made of fractals. The equation to generates it related to another set of fractals called the Julia sets with can a be found within it. For those that don't know intense mathematical magic, to generate the set I convert a coordinate on the screen to a fancy number that I put into a fancy function over and over and get a new number for each pixel on the screen. I then use a second function to convert the number into a full statration color.
For those that can keep up, the Mandelbrot Set is a map of the convergence or divergence of all points in the recursive series zn+1 = zn2 + c in the complex number plane. To generate the set I take a coordinate on the screen and convert it in to a complex number “c”. I then make a loop where I step one iteration through zn+1 = zn2 + c where z0 = c and then add up the components of zn+1 and see if it is over 50. If it is over 50 I conclude it’s diverging so I stop looping and color the pixel based on the number of iterations it took to get to 50, else I continue looping. If I go 25 times and it’s not over 50 I conclude it’s converging and color the pixel black.
It took me 2 tries to make this work at all and it still doesn't look right because it was made while I was at a robotics competition and I was getting impatient. The problem stems from rounding errors in the JavaScript and not enough iterations; it causes the set to be slightly malformed and made of cool "swooshes" as I've decided to call them.
*note: drag to move around the viewer and scroll to zoom*
Sierpiński triangle
This project got started went one of my friends told me that one of his old teachers made the Sierpiński triangle by making random dots or something. He did actually know the mechanism but I figured that meant it couldn't be that hard. A Sierpiński triangle looks like if you were to take a triangle and remove a triangle from it where its vertices were the mid-points of the sides of the original triangle. This will form 3 more triangles, repeat the prosses on the new triangles and you will slowly see the fractal forming.
Because my version uses random dots to generate the triangle it tends to be slow so you will have to give it a moment to load if you check it out. Unlike many of my projects, this one is not interactable.
3D Plotter
This is a Desmos graph I made to understand the transforms for Block and Graph Land.
Calculate Pi
This project was for my 2018 Pi day celebration (3/14). This was originally written in code.org but earlier this school year, to practice my JavaScript, I converted it for uses in the browser.
The first 4 digits (3.141) generate fairly quickly but you have to wait at least 30 minutes to reach the 9.