// Get the button.

window.onload = function() {

document.getElementsByTagName(“button”)[0].addEventListener(“click”, function() {

doMarkov();

});

}

// Define the initial vector.

var x = 11;

var y = 63;

// Define the matrix.

var matrix = [[0.6, 0.8],

[0.4, 0.2]];

// A function to perform a Markov step

// and print the results.

function doMarkov() {

var newX;

var newY;

newX = x*matrix[0][0] + y*matrix[0][1];

newY = x*matrix[1][0] + y*matrix[1][1];

x = newX;

y = newY;

console.log(“x, y: ” + x + “, ” + y);

}

I did this today with my Year 12 Maths C class in Queensland and it was very successful. I have a class of 17 and we used our calculators to generate random digits (potentially not truly random as some students ended up with the same sequence of values – but a good side discussion happening there) and we walked through 10 stages of the first situation given. Students made good observations around what was occurring and predictions of what would happen if we had a larger group and walked through a larger number of stages.

Thank you for sharing! And thanks to Jim at QUT that pointed me in your direction. ]]>

And yes I agree the natural numbers/integers are very interesting! ]]>

The distinction between moving along a line versus moving/rotating in a plane is a big difference between real number and complex number geometry, but it is ultimately about single-coordinate geometry rather than two-coordinate geometry like I’m considering here.

I am having a lot of trouble imagining and understanding your disk description. I dare say I might need a picture of some sort to understand what you mean? Also are you talking about the complex plane of numbers a+bi, or are you talking about the plane with complex coordinates (a+bi, c+di)?

]]>I am wondering if you had any critics?

I am also wondering if you considered the main difference between real numbers and complex numbers: moving along a line vs rotation!

I always thought about complex plan as a disk orthogonal to the x-axis. That disk-iplane has only one point in common with the y-axis, the origin 0.

Imagine it as standing on then caretsian plane, in front of you there is a glass disk when you press the i button on the x-axis to emerge in a rotation similar to peacock feathers display.

How can that i-disk touch the real plane outside of the x-axis?

]]>