IB Maths Resources from Intermathematics
IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides
Chaos and strange Attractors: Henon's map Henon's map was created in the 1970s to explore chaotic systems. The general form is created by the iterative formula: The classic case is when a = 1.4 and b = 0.3 i.e: To see how points are generated, let's choose a point near the origin. If we take... Continue Reading →
Modelling more Chaos This post was inspired by Rachel Thomas' Nrich article on the same topic. I'll carry on the investigation suggested in the article. We're going to explore chaotic behavior - where small changes to initial conditions lead to widely different outcomes. Chaotic behavior is what makes modelling (say) weather patterns so complex. f(x)... Continue Reading →
Modelling Chaos This post was inspired by Rachel Thomas' Nrich article on the same topic. I'll carry on the investigation suggested in the article. We're going to explore chaotic behavior - where small changes to initial conditions lead to widely different outcomes. Chaotic behavior is what makes modelling (say) weather patterns so complex. Let's start... Continue Reading →
This is another fascinating branch of mathematics - which uses computing to illustrate complexity (and order) in nature. Langton's Ant shows how very simple initial rules (ie a deterministic system) can have very unexpected consequences. Langton's Ant follows two simple rules: 1) At a white square, turn 90° right, flip the color of the square,... Continue Reading →