Fractal Searching For The Mandelbrot In Higher Dimensions 29 Sep 2020 — 10 min read Original: https://www.setzeus.com/community-blog-posts/mandelbulb-three-dimensional-fractals Previously, we covered the history & the basics of iterating complex numbers in hopes of generating fractals. Starting from scratch with Julia Sets, we worked our way through defining & plotting the eminent Mandelbrot Set — arriving at the ground-breaking heart […]
Here we crack a tricky yet simple problem at the intersection of computer science and mathematics. It also gives a lovely insight into how to prove something is impossible. Statement and understanding Let’s take a look at the chessboard below. As a warm-up, can you see how to tile it with 2×1 rectangular and 1×2 […]
It’s one of the best-known thought experiments in physics. A cat is placed in a sealed box with a vial of lethal cyanide gas which will be released if a radioactive atom is detected to have decayed. Since the decay of the atom is probabilistic, quantum mechanics tells us that we can describe the cat […]
Infinity There are Different Kinds of Infinities From Brilliance to Madness Philosophy Beginner’s Guide to Mathematical Constructivism The foundational crisis in mathematics along with roughly four decades following it, was likely the most fertile period in the history of logic and studies in the foundations. After discovering the set-theoretic paradoxes, such as the paradox of the set […]
Adding probabilities and velocities have at least two things in common — a maximum and Pascal’s triangle. Introduction Firstly, I know I will be disappointing some but reassuring others that this is not about Relativistic Quantum Mechanics. If you are comfortable with basic algebra, you should find it fairly easy to follow this article. If you’re […]
How to Estimate the Number of Aliens in the Milky Way The so-called Drake equation is a probabilistic argument purposed to estimate the number of active, communicative extraterrestrial civilizations in our galaxy. The equation is: where R* represents the average rate of star formation in our galaxy fp is the fraction of stars that have planets ne is the fraction […]
The inception of quantum mechanics can essentially be traced back to a single “Golden Age” in the mid-1920s at one university: the Georg-August University of Göttingen, in the city of Göttingen in Germany. Home to many notable scientists, the university is associated with no less than 45 Nobel Prize winners. Included in this group are many of the […]
Analysis Represent an ordered pair of integers with a single integer. Represent an ordered pair of integers with a single integer. I wanted to create a lookup table for the coordinate points in the first quadrant of a graph. Searching the look up table would be optimal if instead of storing the coordinates as a […]
Why more (random) testing doesn’t equal better results With the current Corona Crisis going on the world, many people demand more testing. But from a mathematical point of view, just randomly (!!) testing more is not the answer. The problem here lies within the false positives that may occur when two very unlikely events are […]
Leonhard Euler (15 April 1707–18 September 1783) was a Swiss mathematician, who is considered to be one of the greatest mathematicians of all time. He is also considered to be the most prolific mathematician ever, who wrote more than 500 books and papers during his lifetime, filling more than 90 volumes, comprising of over 25000 pages! […]
“Everything should be made as simple as possible, but no simpler.” The special theory of relativity is without question one of the most important discoveries in the history of science and second only to Newton’s discovery of the laws of mechanics in its importance to physics. In spite of this, special relativity is poorly understood […]
In this short introductory article, I will take you on a little journey into the exotic world of prime numbers. It all started in France with the birth of a boy, that was to become one of the greatest scientists, philosophers, and mathematicians of his time. Marin Mersenne was born on 8 September 1588. He […]
It is very likely that, if you regularly read textbooks or research papers on Mathematics, Computer Science or related fields, at some point you stumbled upon what is known as the harmonic sum, which is simply the following sum: The number H(n) is called the n-th Harmonic Number. Besides appearing in many different applications (see, e.g., one of my […]
Now it’s time for a breakdown… (cue En Vogue’s My Lovin’ (You’re Never Gonna Get It)) In particular, a breakdown of numbers! Today we’ll be talking about partitions of numbers. At first glance, they’re a fairly simple concept: a partition of a positive number n is a way to break it up into a sum of positive integers. […]