Geometrical mosaic



Our holiday cottage in Lindos has this wonderful mosaic in the floor. It's made from black and white pebbles each about 2cm in diameter which gently massage your feet as you walk over them. In the doorway the same pebbles write out the date 1908.

Looking at a design like this I can't help trying to reverse engineer it.  The first thing you notice is that the edges of the white quadrilaterals share a straight line with the edges of the black ones.  In fact all the shapes other than the concentric circles are formed by intersecting chords of the outer circle.

The next observation is that these chords come in parallel pairs which are tangent to the inner circle on opposite sides.  These observations are enough to generate a recipe:


  1. Draw the outer circle
  2. Mark every 20 degrees to split into 18 equal parts
  3. Draw a chord between point n and point n+8
  4. Repeat for n = 0...8
  5. Draw the inner circle
I had a go at this using Handwrite Pro on my phone. I ended up using a slightly different recipe because it can only draw horizontal and vertical lines (unless you use freehand) and can only rotate images through multiples of 22.5 degrees:


Comments

Post a Comment

Popular posts from this blog

How To Make ASCII Diagrams Beautifuller

Image
I've discovered an excellent tool in asciiflow.com .  The website makes it really easy to create ASCII box diagrams like this They put these things in fruit machines you know! This is ideal for source code banners, which I think should contain helpful documentation - but most programmers think it's a good place for the COPYRIGHT information and nothing else. But wait! we can make it beautifuller... and easier to read... by replacing some of the ASCII characters with ones available in UTF-8: There!  Isn't that better?  (Although some purists may object to non-ASCII characters in your code base.) SOURCE CODE: #!/usr/bin/python2 # coding: utf-8 # + gets converted in different ways depending on it's 4 neighbours # # . N . { nsew(N,S,E,W) has bit 3 set if N in "+|<>" # W + E { nsew(N,S,E,W) has bit 2 set if S in "+|<>" # . S . { nsew(N,S,E,W) has bit 1 set if W in "+-^v" # { nsew(N,S,E,W) has bit 0 set if E in
Read more

Calculation of ECS using simple convection model

Image
Contents Intro Simple stratified model Alternative convection model Tropospheric temperature gradient Approach used in convection model Calculation of Radiative Forcing from CO₂ increase Calculation of Radiative Forcing from H₂O increase Calculation of zero-feedback ECS Effect of including feedbacks Effect of water vapour Effect of cloud cover change Effect of sea ice loss Calculation of ECS including feedbacks Limitations One more thing: Changes to Troposphere depth Intro The goal of this post is to see if we can come up with an estimate of Equilibrium Climate Sensitivity using a simple model in which the atmosphere is treated as well-mixed.  By "simple" I mean that using the model will not require any advanced mathematics or computation, but will still be realistic enough to come up with an estimate within the likely range of 2.5 - 4.0°C predicted by the IPCC Assessment Report 6 .  I will try to take as little on trust as possible and show how the results are arrived at.
Read more

Why growth is falling in all developed countries (as a long term trend)

Image
In this post I argue that economic growth is not the normal state of affairs, it is a blip caused by the discovery of a one-off resource of non-renewable energy.   The logistic equation $$ \frac{dy}{dt} = y(1-y) $$ Here's a simple model.  Humans discover an exploitable but limited resource and start consuming it.  The amount consumed, $y(t)$, is a function of time.  The general form of the equation is $\frac{dy}{dt} = \alpha y (\beta - y)$, but if you choose the right units $\alpha$ and $\beta$ both become $1$. Why should this work, in principle? Early on, the factor $1-y$ is approximately $1$ and can be ignored.  So the model states that annual consumption $dy/dt$ starts off proportional to $y$.  In other words, $y$ grows exponentially at first.  This could happen if exploiting the resource enables further exploitation of the resource.  For example, suppose a few humans are shipwrecked on an island with 1000 trees: they take ages to cut down the first tree as they are using their
Read more