Tag: loop

The Langton’s Ant

By Anupum Pant

Think of a cell sized ant sitting on a huge grid of such white cells. The thing to note about this ant is that it follows a certain sets of simple rules. The main rule is that when the ant exits a cell, it inverts the colour of the cell it just left. Besides that:

  1. If the ant enters a white square, it turns left.
  2. If it enters a black square, it turns right.

Here’s what happens if the ant starts out in the middle and moves to the cell on the right, as a starting step (this can be on any side).

First step, it goes to the right.
First step, it goes to the right.
Enters a white cell and rule 1 kicks in. The exited cell is inverted in colour and it turns left.
Enters a white cell and rule 1 kicks in. The exited cell is inverted in colour and it turns left.
Enters a white cell and rule 1 kicks in. The exited cell is inverted in colour and it turns left. (Again)
Enters a white cell and rule 1 kicks in. The exited cell is inverted in colour and it turns left. (Again)
Enters a white cell and rule 1 kicks in. The exited cell is inverted in colour and it turns left. (Again)
Enters a white cell and rule 1 kicks in. The exited cell is inverted in colour and it turns left. (Again)
Enters a black cell and rule 2 kicks in. The exited cell is inverted in colour and it turns right.
Enters a black cell and rule 2 kicks in. The exited cell is inverted in colour and it turns right.
Rule 1 again and so on...
Rule 1 again and so on…

Now as this continues, a seemingly random figure starts taking shape. The black cells are in total chaos, there seems to be no specific order to how they appear on the canvas. (of course the pattern is always the same chaos, considering the ant starts on a blank array of cells).

And yet, after about 10,000 steps are completed by the turing ant, it starts creating a very orderly highway kind of figure on the canvas. It enters an endless loop consisting of 104 steps which keeps repeating for ever and creates a long highway kind of structure.

Suppose, initially you take a configuration of black spots on a canvas (not a blank white canvas). Take an array of cells with randomly arranged black spots, for instance. If given enough time, the ant ultimately always ends up making the looped highway. However, before it starts doing it, it might take a significant amount of steps less, or more, than the ~10,000 steps it took to reach the loop in a blank array of cells.

No exception has ever been found. A computer scientist Chris Langton discovered this in the year 1986.

Shepard Tone – An Incredible Auditory Illusion

By Anupum Pant

Here’s the thing. Go to ToneDeafTest.com and take that little test they have on their homepage. That is what you need to do first. Stop reading further if you haven’t done it yet.

Assuming you did what I asked you to do…
If you did well in the test (with a few silly mistakes which can be ignored), you’ll probably understand better what I’m talking about in the following article. Otherwise, you might miss the point.

Nevertheless, there is still a chance that you’d understand even if you are tone deaf. I’m not sure because I’m certain not tone deaf and it’s impossible for me to understand the subjective experiences of tone deaf people (I can boast that the first time I took it, I got a perfect score in that test). Anyway, that test is a fun thing to do. You’ll at least learn something about yourself.

The endless stairs and the endless tone

Everyone knows the endless stairs (in the picture below). Now, you’d think why is the author talking about a visual illusion just after he told us to take an auditory test. That is because the popular visual illusion helps you to relate better to a relatively lesser known auditory illusion.

endless stairs illusion

If you start going up on the endless stairs, you always keep moving up. Even after you come back to the same place, you still keep going up. An impossibility. But it’s something that fools your eyes. The same thing happens if you start going down the stairs.

A similar thing can happen with tones. Listen to the following (continuous?) note sweep.

It sounds like a tone that is continuously going down, endlessly. Only, it isn’t. It’s actually a much smaller looped sound that starts from a high point and then goes down. These little loops have been placed one after the other. If you do not carefully listen to it, you’ll never find the exact point at which one loop ends and the next loop starts. You’ll always interpret it as a continuously going down sound. Just like the continuously going down stairs. This is called the Shepard tone.

This works for discreet notes also. Listen to this endless mario stairs video to get an idea how it works for individual notes (not sweeps).

Why?

Notes are not simple frequencies. A single note is usually composed of several other frequencies. To not overwhelm us with data, the brain puts all these frequencies together and we hear a single sound (note).

Also, our brains like continuity. So, it cherry picks the frequencies from the loop’s notes that makes us hear a continuous sweep. This is the reason we hear no individual loops. Bah! I’m not very good at explaining this. So, here goes the Vsauce video which explains it better. Note that the arrows in the video are the frequencies I was talking about…

The Sun’s Unusual Behavior – Seen from Mercury

by Anupum Pant

The sun – as seen from Earth

For most of us living on Earth (closer to the equator), the sun has followed a simple path throughout the years. It rises, goes up at noon and then sets for rest of the day. It is a simple straight line for the complete year.
For people living a little away from the equator, things get a bit interesting. There, the summer sun at noon is overhead, but the winter sun is low at noon, not overhead. It isn’t very easy for a person living near the equator to grasp this phenomenon well. You’ll have to go there and see for yourself. Or simply, the simulator at the end of this paragraph will help you understand it better.
At poles, the sun almost moves horizontally for many days. It keeps on making a horizontal circle around you. There, it is day for 6 months and night for the next 6 months. [Here is a sun path simulator for Earth]

However, nowhere on earth, things get as interesting as they get in the skies of Mercury.

The sun – as seen from Mercury

On Mercury, the sun appears to briefly reverse its usual east to west motion once every Mercurian year. The effect is visible from any place on Mercury, but there are certain places on its surface, where an observer would be able to see the Sun rise about halfway, reverse and set, and then rise again, all within the same day. It is indeed an unusual performance which isn’t easy for us Earthlings to digest. [See animation in the next paragraph]

Why does it happen?

Let us consider a simpler analogy – some planets (like Mars), as seen from earth, take a similar path. [see the animation for Mars’s path as seen from earth]

The planets, including Earth, all travel around the Sun in a continuous orbit. We can see them make their way across the sky in a straight line usually. However, every now and then a planet appears to turn around. After turning around, it appears to move back the way it came. This is called a retrograde orbit and is caused due to the difference in speeds at which the planets circle the Sun.

So, as we see Mars do a reverse from earth, a similar motion of sun is observed from the surface of Mercury.

[Apparent Retrograde Motion – Wikipedia]