Math

This calculator takes a standard film developing time and adjusts it for temperature. Obtain the nominal developing time and temperature from a data sheet or from the Massive Dev Chart, then enter those values together with the actual temperature.

The calculation follows the exponential temperature correction used on the original Bandicoot calculator:

Here \(T\) is measured in Celsius for the calculation, and \(\alpha = 0.1\). Constant agitation applies the same 10% reduction used by the original calculator. The result is intended as an approximate guide for Ilford black-and-white film/developer processes; other combinations may vary.

Leslie Matrices:

Leslie Matrices are used to model growth (and decline) of age-structured populations. In the model named after Patrick H. Leslie (1945), we have \(N\) age classes, and record how many individuals are in each. Each time period, individuals either age into the next class, or die. The survival rate describes the proportion that moves on to the next age class, and the birth rate, or fecundity, describes the rate per capita of births arising from each age category.

Examples of using sigma.js to do a little graph visualisation.

A SERN is a natural generalisation of a random network, taking into account that many physical networks are embedded in space, and longer links are more costly, and hence less likely.

We’ve been doing some work on SERNs for a little while. Here’s a few relevant links.

A Reuleaux triangle is the shape you get, starting from an equilateral triangle, and adding three circular arcs, drawn from each corner. It’s not actually a triangle, but what’s in a name?

The interesting thing is that a Reuleaux triangle is a shape of constant width. That means it can be used as a roller (but not a wheel). The animation below shows this – we can see that although the centre of the triangle moves up and down, the top surface of the rotating triangle is always level.

Follow the link below to see more, get links to 3D printable versions, and Matlab code to play with it.

A couple of little tools for playing with Catenaries can be found at: http://bandicoot.maths.adelaide.edu.au:3838/catWorkshop/, and http://bandicoot.maths.adelaide.edu.au:3838/catenary/. They aren’t really documented yet – they’re just a toy to play with Shiny – but more will come later.

Leslie Matrices are a tool for modelling population demographic dynamics. Wikipedia does a decent job of explanation of these. My megre contribution is a little online Leslie Matrix Calculator.

Links to code from projects or math topics.

• conSERN: fast generation of Spatially Embedded Random Networks (SERNs).
• mgtoolkit: a Python toolkit for Metagraphs.
• LinePicking: code for solving the Line Picking problem.
• AutoNetkit: Automated network configuration toolkit
• Topology Zoo: a project to collect and transcribe data network topologies from around the world.
• COLD: network topology synthesis.
• SAIL: Statistically Accurate Internet Loss Measurements.
• Roulette code is available from GitHub, or via the Zip file listed below.
• latexFromExcel is a little tool to incorporate Excel table information into a LaTeX document flexibly. Its Perl – live the dream :) Or at least don’t complain – I’m not going to rewrite in Python.

I’m getting into Julia, which is cool. Here’s a few snippets resulting from my attempts to learn it

A Log-azimuthal map of the world (as seen from Adelaide, Australia, my home town) using log-distances, is a map that shows places close by are displayed in detail, and those further away, have less.

There are a large variety of sea-shells (and land shells) that can be simply described by rotating a ellipse around a log-spiral that has been projected onto a cone. The image below was generated using this approach:

All class details and materials are obtainable from the links below.

Before you get there though, a quick work on diversity and inclusion:

My Personal Commitment to Diversity and Inclusion

I acknowledge and honour the fundamental value and dignity of all individuals, and I am committed to fostering a respectful and inclusive environment in this course.

We are diverse by nature and inclusive by choice, and the diversity students bring to our university is a resource, strength and benefit.

A Roulette is a curve derived by rolling one curve against another. In the image below, the blue point on the blue ellipse is rolled along a straight line (the x-axis) to generate the purple curve (which is called an undularly).

Included here is some Matlab code to generate roulette curves, with a fair degree of generality, but also showing how to generate specific instances such as cycloids, trochoids, the Cissoid of Dioclese, and the undularly and nodary.

SAIL, short for Statistically Accurate Internet Loss Measurements, is a method for rigorous statistical analysis of packet-loss measurements. It uses algorithms from Hidden Semi-Markov Models to estimate the parameters of the underlying loss process from measurement traces, then computes the loss rate and its variance.

The method is designed to be light-weight: the main algorithms run in linear time in the number of measurement samples. This page collects the SAIL MATLAB implementation, usage notes, sample-data information, and related papers.