maths and computing experiments
About PenroseKiteDart Below we present some animations that illustrate operations on finite patches of Penrose’s Kite and Dart tiles. These were created using PenroseKiteDart which is a Haskell package available on Hackage making use of the Haskell Diagrams package. For details, see the PenroseKiteDart user guide. Penrose’s Kite and Dart tiles can produce infinite aperiodic […]
Introduction (Updated June 2026 for PenroseKiteDart version 1.10) PenroseKiteDart is a Haskell package with tools to experiment with finite tilings of Penrose’s Kites and Darts. It uses the Haskell Diagrams package for drawing tilings. As well as providing drawing tools, this package introduces tile graphs (Tgraphs) for describing finite tilings. (I would like to thank […]
We continue our exploration of properties of Penrose’s aperiodic tilings with kites and darts using Haskell and Haskell Diagrams. In this blog we discuss some interesting properties we have discovered concerning the , , and operations along with some proofs. Index Quick Recap (including operations , , on Tgraphs) Composition Problems and a Compose Force […]
We have been exploring properties of Penrose’s aperiodic tilings with kites and darts using Haskell. Previously in Diagrams for Penrose tiles we implemented tools to draw finite tilings using Haskell diagrams. There we also noted that legal tilings are only correct tilings if they can be continued infinitely and are incorrect otherwise. In Graphs, Kites […]
Graphs, Kites and Darts Figure 1: Three Coloured Patches Non-periodic tilings with Penrose’s kites and darts (An updated version, since original posting on Jan 6, 2022) We continue our investigation of the tilings using Haskell with Haskell Diagrams. What is new is the introduction of a planar graph representation. This allows us to define more […]
Figure: leftFilledSun6 Update June 2026 This blog is about drawing finite regions of the infinite non-periodic tessellations of Roger Penrose’s kite and dart tiles. It was first written before developing a Haskell package (PenroseKiteDart) now available on Hackage. More info and developments can be seen at the end. I have made small updates to this […]
Multigrid Methods with Repa Introduction We implement the multigrid and full multigrid schemes using the Haskell parallel array library Repa. Whilst this file is a literate Haskell program it omits some preliminaries. The full code can be found on GitHub at multiGrid. Repa (short for ‘regular parallel arrays’) is a Haskell library for efficiently calculating […]
Red-Black Neighbourhood Stencil Diagrams (for Laplace) In a previous blog Repa Laplace and SOR, I used Repa to implement a Laplace solver using the Red-Black scheme. The explanation of alternating stencils probably needed a diagram, so here it is. This diagram illustrates the shapes of the stencils for adding neighbours of red and black cells. […]
Using the Repa Library for Laplace’s Equation and SOR This describes the result of some experiments to enhance an existing elegant (haskell parallel array) laplace solver by using successive over-relaxation (SOR) techniques. The starting point was a laplace solver based on stencil convolution and using the Haskell Repa library (Regular Parallel Arrays) as reported in […]