Infinite Limits

The Mandelbrot Set is a set of complex numbers commonly used in art, due to its mathematical beauty. It was first defined by Robert W. Brooks   and Peter Matelksi in 1978, and the first visualisation was made by Benoit Mandelbrot in 1980.   Credit: American Scientist A lot of websites, videos, applets, and so on do a repeated zoom into the boundary of the Mandelbrot Set. But in mathematical terms, we define the Mandelbrot Set as the set of complex numbers which (under iteration) stays bounded within two. Here’s how it’s mathematically represented (don’t skip this, it’s easy math): f c (z) = z 2 + c, f c (z)<= 2 Let’s take an example here to understand this.   If c=-2,   f -2 (0) = 0 2 + (-2) = -2 (You start with z=0 as default) f -2 (-2) = (-2) 2 + (-2) = 4+ (-2) = 2 (You take the result of the previous function and input it as z in the next iteration) f- 2 (2) = (2) 2 + (-2) = 4+ (-2) = 2 We know that the result of the previous function (2), upon another itera...

 Hey! I (Shikhar) am a high school junior, currently studying at The Cathedral and John Connon School, Mumbai. I've always had a strong passion for mathematics, so I decided to start this blog. Here's a bit about me. Through my time in school and at home, I've taken to subjects such as mathematics, physics, economics, and finance. Consequently, I often spend my free time reading about the latest happenings in these fields. Academics aside, I play the viola, write poems, swim, run, and play basketball in my free time. I enjoy watching tennis and NBA games regularly, and enjoy shows like  Community ,  The Office,  as well as some anime. Listening to hip hop and jazz has become a daily routine for me, at this point. That's enough about me - on to the blog. Infinite Limits is a blog that aims to cover topics I find interesting in science, technology, engineering, arts, and mathematics (STEAM). The idea for the name of the blog stems from the topic of limits in mathematic...