If you’re familiar with computers , electronics and programming, you have probably learn things about binary systems.
The goal of this study is to build a graphic representation (with Processing) of binary numbers on a matrix strip. Thereby we will see if an “architecture” or a “pattern” could emerge.
The software will plot binary numbers on rectangular boxes. From 0 to 64 , on 8 Bits. An high-state bit is White and a low-state bit is Black.
Logic Strip on 8 bit from 0 to 64.
The strip needs to be read from top to down. The first line equal to 00000000 , the second 00000001 , the third 00000010 , etc…
The first thing we can see is that it make a tree-shaped diagram. A pattern seem to exist in both horizontal way (with this step-shaped serial) and vertical way with a x2 plotting for each bit (1:1 for first bit ; 2:2 for second bit , 4:4 for third bit , etc..).
This shape is inherited from the 2^n structure of the binary system. At this step , i think that the first results are very interesting but we can dig more with this logic strip.
Now, the objective is to evaluate the type of change produced by a multiplication (the “addition” only shift the strip vertically , repeating the template again and again).
Up : [0:64] x2 ————— Down : [0:64] x4
Here we find something that some people have already noticed : a x2 multiplication => shift by one bit. Naturally , the x4 is like 2×2, so two shifts are visible. However , the architecture haven’t changed, only the shift appear.
Up : [0:64] x3 ————— Down: [0:64] x5
The x3 and x5 , are way more complicated to study. It’s quite difficult to draw an horizontal pattern , but the vertical pattern is clearly visible (and it is different in each strip). The pattern seem to be 1:1:2:1:1:2 or 1:2:2:1:2:2.
For the fun , let’s do x6 . If we’ve worked well , it’s need to be like 2×3 :
Bingo ! 😀
And with a x*x way (0*0 , 1*1 , 2*2 etc…) ?
That is a cool one n_n. We clearly see the “V” shaped evolution in horizontal and a vertical behavior graphically interesting . (Remember that it still need to be read from up to down ! 0,1,4,etc..)
Those “Logic Strips” are interesting (and quite artistic) ,but the best thing will be to discover if any algorithmic behavior could simplified , or better understood.
To continue this study , the graphical concept will be adapted in a “logic gate” way , for building a “mapping of changes” . That could allow us to see logic operation in another way.
But it’s for the second part ! Stay tuned :3