Pictures of Pi

Rectangular bitmap

• 262144 bits of binary Pi ordered as a 512 x 512 bitmap. 0 = black pixel. 1 = white pixel. The bits are ordered from left to right in each row and the rows from top to bottom. (41K)

• The bitmap blurred. (17K)

• Blurred with higher contrast. (30K)

• Blurred with even higher contrast. (46K)

• Blurred with very high contrast. (only 5K)

• Blurred and run through an edge detector. It's too dark, so we... (18K)

• ...increase the contrast. Spaghetti? (55K)

• Blurred and posterized. (21K)

• Blurred and then sharpened again. (55K)

• Blurred and run through a threshold function. (18K)

• The bitmap run through a despeckle function. (29K)

• Despeckled and then edge detected. (62K)

Diagonal bitmap

• 131328 bits of binary Pi in a bitmap where the bits are ordered like this: until the diagonal from the lower left corner to the upper right corner is filled (i. e. the red area below the diagonal will be empty). 0 = black pixel. 1 = white pixel. (23K)

• The bitmap blurred. (14K)

• Blurred and extra contrast. (27K)

• Blurred and edge detected. (27K)

• Blurred and run through a threshold function. (16K)

Pi Walk 1 (28K)

Algorithm:

Place yourself with your face to the north.

Go through the 65536 first bits backwards and do like this:

• If the bit is a 0, then walk one pixel forward and turn left.
  If the bit is a 1, then walk one pixel forward and turn right.

• Draw a pixel where you are standing.
  The closer you are to the beginning of Pi, the lighter the color.

The background has the colors it has because I like sunsets!

I have also made a 3D-movie (105K) with this method.

Pi Walk 2 (19K)

Algorithm:

Group the 65536 first bits two by two. Then every group can assume a number from 0 to 3:

00 - 0
01 - 1
10 - 2
11 - 3

This is actually Pi encoded into base 4. Then, go through the sequence of base 4 digits backwards and do like this:

• If the digit is a...
  0, then walk one pixel to the east
  1, then walk one pixel to the north
  2, then walk one pixel to the west
  3, then walk one pixel to the south

• Draw a pixel in the new position. The closer you are to the beginning of Pi, the lighter the color.

Circle

(only 2K)

The simplest visualisation of Pi is probably a circle.

Half the circumference of a circle with radius 1 is exactly Pi!
The area inside that circle is also exactly Pi!
Isn't that fascinating?

I'm planning to make more pictures with more complicated techniques. I have many ideas...

Do you have any ideas of how to visualize Pi? Tell me!