Maths in 60 Seconds Online Competition

Competition

You’re invited to submit entries for our online #IMA60 anniversary competition!

The theme is #IMAMathsin60seconds – share some interesting mathematics in under 60 seconds. Your topic can be anything from the wonderful world of mathematics. Be creative and choose any supporting media you like: videos, animations, text, images, or something else!

All you need to do is post your entry on social media, tag the IMA and use the hashtag #IMAMathsin60seconds.

Prize

Entries will be judged by a panel and the winner and runner up entries will be showcased at our anniversary event at the IET in London on 16th October. The winner will also receive an IMA Goody Bag and Amazon voucher worth £75.

Closing date 6 October 2024.

Check out our launch video and accompanying example below:

The Lorenz Equations – 60 Years of Chaos
Last year (2023) marked 60 years since mathematician and meteorologist Edward Lorenz discovered a beautiful emergent behaviour from a system of differential equations. The time-dependent Lorenz equations are a simplified model of cellular convection in three dimensions, designed for use in weather prediction. The result Lorenz discovered (coined the ‘butterfly effect’) relates to the sensitivity of a system with respect to its initial conditions. For a given combination of system parameters, very small changes in initial conditions may lead to erratic dynamics, which are aperiodic but attracting. This phenomenon is known as ‘chaotic behaviour.’

In this animation we solve the Lorenz equations [1]:

𝑑𝑋/𝑑𝑡 = 𝜎(𝑌 − 𝑋)
𝑑𝑌/𝑑𝑡 = 𝑋(𝜌 − 𝑍) − 𝑌
𝑑𝑍/𝑑𝑡 = 𝑋𝑌 − 𝛽𝑍

with parameters values: 𝜌 = 28, 𝜎 = 10 and 𝛽 = 8/3.
Two very similar initial conditions are specified: (𝑋, 𝑌, 𝑍) = (1,1,1) & (1,1,1.01) and the solutions are seen to diverge as time progresses.
Solutions of the Lorenz equations have been extensively studied, and a huge number of resources may be found online.