Flights of the butterfly

  • Langton’s ant

    This is Langton’s ant. He lives on a plain sheet of paper, preferably white, with squares on it. His name is possibly Cyril. But, it could be Rodney. It’s difficult to tell. •           Cyril, or possibly Rodney, likes an uncomplicated life. He lives by just two rules. •           And two pots of paint. THE RULES…

  • Intersections and other stuff

    Here are three lines intersecting at a point: Well, actually, it’s not. As any engineer will tell you, it isn’t quite like that, it looks like this: There is always a slight error. In fact, when you get closer, it looks like this: Actually, nobody ever drew a straight line anyway, they all look like…

  • How big is infinity?

    This seems a silly question. You would think the answer is “bigger than that.” But take a look at this: All of these sequences go on “forever” (we’ll get back to that later) So they are all infinite series. But, logically, the lower rows seem to have fewer numbers than the “all” row. These are…

  • Global Warming

    OK, baby stuff is over. I don’t care who this offends. And I don’t care if nobody reads it. At least I will know I have put it out there. SO FAR SO GOOD For several thousand years, humans have been extracting energy from the environment directly. They have done this through three methods:  So…

  • The Universe and ATC

    This information can be represented on a spreadsheet: