Visualizing Pi

Pi, base-3 and base-4

artieeee — Fri, 23 May 2008 09:57:23 +0000

Pi in base-3 with 19000 digits:

Pi in base-4, 8000 digits:

How would pattern look like?

artieeee — Fri, 23 May 2008 09:23:58 +0000

What if there was some encoded pattern in the Pi or any other number, how easily we could detect it? I made a small demonstration for this. I used the Pi with 10000 digits and created a small but detectable zig-zag-pattern in it. But you can only see it when the columns are configured in certain way. Here, both images represent the same number but they have different column-size. Can you see which one of the images has that pattern? (Click to enlarge)

Ok, here are both pictures with only the color blue selected:

This small demonstration shows that it would be very difficult to actually find some encoded information from Pi or some another number by just visualizing data. Imagine if there was a picture of circle encoded in Pi but it would only appear if the columns were set to 1728 pixels wide. Hard enough, or what if the required column size was 2 985 984 pixels? It would go unseen. Only way we could detect some pattern was if there was some number in the column repeating. For example, if there was a filled circle this would be the case. But for that case you would have to go very far… For example, the digit 0 first appearing 8 times in row is in position 172 330 850. Another thing to consider is that if there was information encoded with another numerical system (like base-12) we couldn’t detect that either.

Phi

artieeee — Thu, 22 May 2008 22:11:12 +0000

This is how Phi (Golden Mean Ratio) looks like, with 20000 digits precision and base-10:

Pi, base-12

artieeee — Thu, 22 May 2008 20:22:22 +0000

Here, Pi with 8000 digits in Base-12 system:

I created the digits with the program “abtestc5“. It is unstable in my computer, so I couldn’t create very large numbers but I also didn’t bother to try with another version.

Introduction to project

artieeee — Thu, 22 May 2008 12:49:10 +0000

Hi !

I decided that I could visualize Pi, just for fun.

Pi is the number that even ancient egyptians did approximate. It represents the ratio of any circle’s circumference to its diameter in Euclidean geometry, which is the same as the ratio of a circle’s area to the square of its radius.

Pi is irrational and transcendental number. Basically it means that Pi is never-ending number.

Pi approximately equals to 3.14159.

What is my aim, is to show how Pi looks if we color-code all the digits in it. For this purpose I wrote a small Java program which does all the work for me.

I copy-pasted the 10 000 first digits of Pi into my program and here is the first result of how Pi looks like. You can save it to your computer if you want a better view of it. Notice that windows-preview does some serious blurring to the image, so if you want the best view you must open it in some graphic-tool, Windows Paint can do.

Here is another view, pixel-size set to 1 and only 12 columns: