In this post we present a high level introduction to evolution and to how we can use mathematical tools such as dynamical systems and Markov chains to model it. Questions about evolution then translate to questions about dynamical systems and Markov chains – some are easy to answer while others point to gaping holes in current techniques in algorithms and optimization.

## Tag: fractals

## Domains of Psychic Perception and Influence

A lot of discussions in typical communities that touch on psychic subjects use words like sensitive, aware, intuitive, etc to describe how a person is psychic. You might hear them describe the information they passively get as a range. You might even hear words such as energy fields. These archetypes also show up in media and literature Those words, phrases, and archetypes are pragmatic within the context of various paradigms – especially energy healing and energy working paradigms; however, they are not very accurate. Instead of fields of awareness, ethereal energy, and sensitivity, you have an ontological realm of knowledge Read More

## Splitting Rent with Triangles

You can find out how to fairly divide rent between three different people even when you don’t know the third person’s preferences! Find out how with Sperner’s Lemma.

## Times Tables, Mandelbrot and the Heart of Mathematics

The good old times tables lead a very exciting secret life involving the infamous Mandelbrot set, the ubiquitous cardioid and a myriad of hidden beautiful patterns. Time for the Mathologer to go on a serious fact-finding mission.

## Lecture 14: Divide and Conquer Recurrences

## Lecture 13: Sums and Asymptotics

## Lecture 3: Strong Induction

## Lecture 2: Induction

## A Computational Introduction to Number Theory and Algebra

The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications.

## The Nature of Code: Simulating Natural Systems with Processing

In this post, there is a playlist of video lectures that supplement the book.

How can we capture the unpredictable evolutionary and emergent properties of nature in software? How can understanding the mathematical principles behind our physical world help us to create digital worlds? This book focuses on a range of programming strategies and techniques behind computer simulations of natural systems, from elementary concepts in mathematics and physics to more advanced algorithms that enable sophisticated visual results.

Read The Book