[Study] Logic Strip & Graphic Mod. [Pt.1]

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.

Tree_base

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).

Tree_2  Tree_4

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.

Tree_3  Tree_5

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 :

Tree_06

[0:64] x6

Bingo ! 😀

And with a x*x way (0*0 , 1*1 , 2*2 etc…) ?

Tree_Carr

[0:64] XxX

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

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