From 742b753a4177a7fcaa09ccbe936a54875c2f0a7f Mon Sep 17 00:00:00 2001 From: potmo Date: Mon, 7 Feb 2022 01:16:24 +0000 Subject: [PATCH] Built the .tex.md files --- readme.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/readme.md b/readme.md index af0b361..8bf99ef 100644 --- a/readme.md +++ b/readme.md @@ -347,7 +347,7 @@ Even if the De Bruijn sequence is efficient at packing information in a sequence -The radial ordering of the sequences (rings) are generally arbitrary. The sequences closer to the middle cover a smaller area since the circumference increases with radius. Since the mirrors might not be totally exact due to the fabrication process it can be a good idea to have more information density in the periphery of the disc where the area are bigger. We could for example sort the sequences in a way such as we put the single color sequences end up close to the middle and the sequences with multiple colors end up close to the periphery. An over engineering method (that I've opted to go with) is to sort the sequences on their Shannon entropy. Shannon entropy of is defined as:

+The radial ordering of the sequences (rings) are generally arbitrary. The sequences closer to the middle cover a smaller area since the circumference increases with radius. Since the mirrors might not be totally exact due to the fabrication process it can be a good idea to have more information density in the periphery of the disc where the area are bigger. We could for example sort the sequences in a way such as we put the single color sequences end up close to the middle and the sequences with multiple colors end up close to the periphery. An over engineering method (that I've opted to go with) is to sort the sequences on their Shannon entropy. Shannon entropy of is defined as:

Where is the possible outcomes which occur with probability . We don't really have to dwell too long on the nitty gritty but can conclude we can compute a number for each sequence that will be lower if not much happens in it and high if there is a lot happening. We can then use that to sort the radial rings. In our example here single color sequences ends up in the middle.