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The Kochawave Fractal
Whilst browsing twitter the other day this tweet caught my eye about a variation on the famous Koch curve fractal and I thought it would be fun to reproduce it in Python (click here to download the Jupyter notebook).
The Kochawave curve, a variant of the Koch curve.
— Luca Moroni (@sfera314) November 1, 2022
Beautiful paper by Rémy Sigrist.https://t.co/Ld0yGRUsn5 pic.twitter.com/FSstqbsBhc
The Kochawave Fractal
Whilst browsing twitter the other day this tweet caught my eye about a variation on the famous Koch curve fractal and I thought it would be fun to reproduce it in Python (click here to download the Jupyter notebook).
The Kochawave curve, a variant of the Koch curve.
— Luca Moroni (@sfera314) November 1, 2022
Beautiful paper by Rémy Sigrist.https://t.co/Ld0yGRUsn5 pic.twitter.com/FSstqbsBhc
Producing videos with manim
I often refer students to the excellent YouTube channel 3Blue1Brown by Grant Sanderson who produces videos that explain various mathematical concepts. To produce these videos Grant wrote the Python library manim and released it for anyone to be able to use. The learning curve is a little steep at first but with the help of the documentation written by the manim community it soon becomes straightforward to create your own videos.
portfolio
publications
The applicability of the shallow water equations for modelling violent wave overtopping
Shiach, J., Mingham, C.G., Ingram, D.M. and Bruce, T. (2004) The applicability of the shallow water equations for modelling violent wave overtopping. Coastal Engineering, 51(1), pp 1 - 15.
Extended shallow water prediction of overtopping
Shiach, J., Mingham, C.G., Ingram, D.M., Causon, D.M., Bruce, T., Pearson, J. and Allsop, N.W.H. (2005) Extended shallow water prediction of overtopping. In Proc. 29th International Conference on Coastal Engineering, Lisbon, Portugal.
Numerical Modelling of wave run-up and overtopping using depth integrated equations
Shiach, J. (2008) Numerical Modelling of wave run-up and overtopping using depth integrated equations. PhD Thesis. Manchester Metropolitan University. Manchester, UK.
A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations
Shiach, J. (2009) A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations. Coastal Envineering. 56(1), pp 32 - 45.
talks
teaching
Numerical Methods for Partial Differential Equations
Undergraduate course, Manchester Metropolitan University, 2020
A third year unit that covers the numerical solution of Partial Differential Equations (PDEs).
Mathematics of Computer Graphics and Virtual Environments
Undergraduate course, Manchester Metropolitan University, 2020
A second year unit that explores the mathematics that underpins computer graphics used in computer games and the TV and film industry.
Computational Mathematics
Undergraduate course, Manchester Metropolitan University, 2021
A second year unit that examines the implementation of mathematics in modern computing applications such as computer graphics, logical ciruits, graph theory and algorithms.
Computational Methods in Ordinary Differential Equations
Undergraduate course, Manchester Metropolitan University, 2022
A third year content that covers numerical methods for solving Ordinary Differential Equations (ODEs) and linear systems of equations.
Graduate Development and Employability
Undergraduate course, Manchester Metropolitan University, 2022
A first year unit that develops students’ employability skills and explores how to study mathematics at undergraduate level.
Computational Mathematics
Undergraduate course, Manchester Metropolitan University, 2022
A second year unit that examines the implementation of mathematics in modern computing applications such as computer graphics used in computer games and digital sound processing.
Linear Algebra and Programming Skills
Undergraduate course, Manchester Metropolitan University, 2022
A first year unit that introduces students to linear algebra, Python and MATLAB programming.