THE EVERYTHING FORMULA
There is a very interesting formula.. Known as the everything formula or the self-referential formula in maths.. Which exhibits few very interesting and absurd properties.. Well.. In this answer i am going to try and explain u the absurd property of this formula..
For all of you who want to know how this formula (inequality rather) looks like..
Here it is..
(those L shaped brackets u see are not brackets but they are floor functions)
Well, now u might be thinking what is so special about this inequality..
The weirdest fact about this formula is that if one graphs the set of points (x, y) in 0 ≤ x < 106 and k ≤ y < k + 17 satisfying the inequality given above for a properly chosen constant k, u can actually graph anything u wish to..
Let me explain u with an example..
Image source - Wikipedia
Guys the above picture is a graph plotted on the x-y plane for a certain 543 digit integer (which i am not mentioning in this answer due to its length :)) . The amazing part is that the graph is the formula itself.. Yes.. Similarly, u can graph anything, any design, any name using this formula on the x-y plane only if u chose the correct constant k.
And finding this constant for any plot u like is not very difficult. It is really very easy if u know how to convert binary numbers to decimal numbers.
For example, let's say i want to plot my name’s initial letter ‘A’ on x-y plane using this formula. So we need to represent the letter in a pixeletted form (which i cannot do so i am just showing a manual drawing which i have done)
As u see, i have marked the blocks as 1 & 0. 0 for the empty ones and 1 for the ones which are a part of the plot. ( i haven't marked all the empty blocks)
So now what u do is, u just jot down the digits from the leftmost bottom block, going upwards upto k+17, and repeating from next column. So the resultant number u get is the binary form of the required no. Now just convert it into decimal and multiply by 17 and you get your desired number.
In this process u can plot anything u like, ur name, any diagram, u can even write a love letter to ur gf ( and that would be great if she understands maths and appreciates ur hardwork) :p
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