For a while I have been doing some elementary dice-walking. My method is thus: I take an A-Z, a protractor, a ruler, a coin and some dice of various shapes. I locate my current location on the map. I then flip the coin, roll a D30 and a D6. If the coin is heads, then I will go east, if tails, then west. The D6 then determines which sixth of the available 180 degrees I will travel. So if heads landed, then a roll of 1 will mean a bearing between 001 and 030. If 2, between 031 and 060 etc. The D30 determines which of the 30 degrees within that sixth. So the following "table" should demonstrate what sorts of outcomes generate what bearings.
Coin---D6---D30---Bearing
Heads---4----25----115
Tails---6----5-----335
Then I roll the D30 again. I divide the outcome by 2 and that is the distance in centimetres I must walk to on my map, at the bearing decided. I have a 15cm ruler. Unfortunately a centimetre doesn't really correspond to anything physically relevant in real life, since the map is 4 inches per mile. That means that the radius of the circle formed by all the possible locations I could walk to is about 1.5 miles. There are 5400 locations that can be generated from just this one trial. If I do this experiment twice, so that I go to one place and then go to another place using the first location as the starting point for the second experiment, there are 291 million possible journeys I can make within what would be a 28 square mile circle. Every unique journey is equally likely. With three separate routes there are over 157 billion journeys I could make in a 63 square mile circle. Also note that it's extremely unlikely I would end up between say 4 and 4.5 miles away from my original location. For that to happen I would need to get similar bearings on each trial and very high values on the D30 distance results. It's clearly calculable, but I'm not sure how. I'd estimate though, that the probability of ending up between 4 and 4.5 miles away from my starting point would be less than 0.00001.
So I was thinking of how to integrate this sort of system into a wider space with greater probabilities. It's actually possible to cover the whole globe, and randomly generate one very specific area on the planet. How specific? Incredibly specific actually. on my primitive protractor model the distance between a result like (H 5 20 23) and (H 5 20 24) is in real terms about 80 metres. Plus I am hardly interpreting the map precisely. I probably end up around 30m away from the exact point specified by the dice and that's about as close as I can get.
Now suppose a system whereby we can generate any metre squared point on the surface of the planet. First off, we would need to generate one of the UTM zones so that we can "zoom in" on some part of the world. Here is a map of the UTM zones.
So there are 1200 of those. Then there is the GPS. A typical GPS measurement looks like this:
18T 0424200 5097850
The 18T represents the UTM zone, so looking at that map we can tell that this is around the New York area, probably with parts of the U.S.A and Canada inside it. The second number is the eastings and the third the northings. Unfortunately these aren't jointly specific to the UTM zone itself. The easting represents the distance east from the meridian, in this case, the 18th. Imagine a map of just 18T and the 18th meridian will be the left or westward border. The northing is the distance from the equator which makes generating a random location now quite problematic. It seems that we can get a random longitude. Each UTM zone is about 667 km long. So there should be a method of randomly determining the UTM zone, and then determining an eastings, i.e. a distance from the meridian. Our problem then is determining our northing. Use of UTM here seems pointless, because the GPS is given in terms of distance from the equator. I'm not sure how to get around this yet. That is all for now.
