# Blog

A blog of Python-related topics and code.

## The Babylonian spiral

A Babyonian spiral (OEIS A256111) is the figure formed by starting with a zero-vector at the origin and concatenating vectors such that each subsequent vector is the next one longer than the previous one that also lands on a position with integral Cartesian coordinates. That is, the $i$th vector has integer components $x_i$ and $y_i$ satisfying, $x_i^2 + y_i^2 = n_i^2 > n_{i-1}^2$. Each vector is chosen such that it minimizes the angular separation from the previous one.

## Hexagonal Truchet tiling

Following on from this earlier post, here is a class, TruchetHexes, which generates a pleasing weave-like pattern by tiling the following hexagon shapes in random orientations.

## Inflation in Austria

STATISTICS AUSTRIA provides economic and demographic statistical services to the state of Austria. This page lists the Consumer Price Index it calculates every month according to a methodology that is updated every five years.

## Quadtrees #2: Implementation in Python

The following code implements a Quadtree in Python (see the previous blog post for a description of quadtrees). There are three classes: Point represents a point in two-dimensional space, with an optional "payload" (data structure associating the Point with more information, for example the identity of an object). The Rect class represents a rectangle in two-dimensional space through its centre, width and height. There are methods to determine if a given Point object is inside the Rect and to determine if the Rect intersects another Rect.

## The double compound pendulum

Following on from this post about the simple double pendulum, (two bobs connected by light, rigid rods), this post animates the double compound pendulum (also called a double complex or physical pendulum): two rods connected to each other, with their mass distributed along their length. The analysis on Wikipedia provides the dynamical equations for the case of equal-mass and equal-length rods. Here, the more general case of rods with lengths $l_1$ and $l_2$ and masses $m_1$ and $m_2$ is considered.