Donald Knut: this is a turnaround

When you enter my house ... uh ... My wife and I wanted us to have any works of art in the house that were personal and also related to what we do. And so you can see two things: one of them is the dragon curve, I will tell you more about it in a minute. And the other is this job. This is a line from Pete Hayn’s “Road to Wisdom”:

Must we
To wisdom
Eternal to get,
What to us
So tempting
Is dawning
Again
And again,
And again
Be wrong
But less often
And less often
And less.
')
This is one of my favorite phrases. A kind of my life story is making mistakes and trying to learn something from them. This phrase was designed in the form of a superellipse, which is one of the great discoveries of Pete Hein. This ellipse is more complete and has been used in many architectural products.




And so, what is the idea of ​​a dragon curve? This is what came into being thanks to a pair of physicists in the late sixties.



Take a piece of paper and bend it, bend it again, and again and you do it n times. N is nine in the case of the dragon curve on the wall to the left.



When you look at it, you see that some of the folds are curved upward, and some inward. If you imagine that you are moving along this curve, then you turn left here, then turn left here, turn left here again, but then you turn right and then another turn right, and again turn left and so on.



This is a left and right pattern. The most amazing thing is that if you continue this curve, do it 9 times, and then open all these folds at an angle of ninety degrees, then you will get a path that starts to fill the space and creates a beautiful practical pattern. Let's start here from this tile, for example.



If you bring the camera closer, you will see that my wife and I wrote our names here, but we can talk about this story later. This curve starts, turns left, left again, then right, then left, then left again, and so on. This is exactly the pattern that you get by folding the paper. Since I folded the sheet 9 times, 512 steps are shown on the wall. Well, probably 511. The curve ends here and it all continues, but in the middle it becomes very confusing.

The wonderful thing about geek art is that you only need three types of tiles.



You need an absolutely empty tile or a tile with only one loop on it, like here, or a tile with two loops on it, like this one. And, of course, I can take a tile with two loops and turn it over, say, in this direction. Then it will not connect here, but it forms an isolated circle here.



I had to calculate how many empty tiles I would need, how many tiles with one loop I needed and so on. We made a mockup of wrapping paper and cardboard and kept it in the apartment where we lived while our house was being designed. And we decided that it was a cool design and it would be cool to have something like this in our house when it was finally built.



We both liked the HIT Ceramics tile in Sausalito, California and we had a design layout, so we went to look at the ceramics and talk to people working there. And we wondered if they could make for the order for us a certain number of empty tiles, tiles with one loop, etc. They replied that yes, they can do it, but they make the tiles a small 3.5-inch square.

And for my design required 2 inch squares. The calculations could not be changed, even if I changed 9 by 8. It would be an interesting pattern, but at the same time it would be huge and would not look normal on such a scale.

This type of pattern is very attractive in this size, and not in a larger size. We apparently looked very upset and disappointed, because the person with whom we spoke saw that we were upset as we drove all this way with this great idea. And he said: “Wait a minute, in June we go on vacation, we close our factory, but we have a guard here.

You can come and use our equipment, we will allow you to use our clay and make tiles. If you are going to cut them to a size of 2x2 inches, then we will cover the tiles with our glaze and we will burn the tile for you. So we did. We went there and spent the whole day there, making all of this tile, including several spare tiles. And we placed our initials on this tile, at the starting point. Then this tile was fired. Some marks from the fire can still be seen occasionally, the tiles in some places cracked a little during firing.



We still had nine of them. After eight steps, the line is here, after 16 here, at step 32, I'm here.

As the years passed, I finally placed a chapter in my book “Fun and Games,” which says so. And I read all the articles on this topic, I wrote about the curve of the dragon and came to the shocking discovery that this * shows the wall * is wrong.



You get this curve at the expense of 9 folds, but I did the 9 fold in the wrong direction. Instead of going this way, I went to the other.



The last half of this curve actually has a different fold. From the point of view of mathematics, I lived with this curve for 30 years and did not realize that I had a mathematical error in design.

- What do you feel about this?
- I felt the meaning of the phrase:

To wisdom
Eternal to get,
What to us
So tempting
Is dawning
Again
And again,
And again
Be wrong
But less often
And less often
And less.

---

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