# Method For Constructing Self Referential Formulas Like Tupper's

Can anyone please explain exactly how formulas like Tupper's self referential formula can be constructed?

I'll like to see the reasoning behind the derivation of such formulas and the steps required to create a new one.

NOTE: I know Tupper's self referential formula is not as 'self referential' as it is claimed but some form of 'universal' formula capable of producing any bitmap of a given size, given the value of N.

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The formula can produce any 17 bit high image. The secret of finding the self-referential image is in the constant $k$, essentially knowing where to look. How to determine $k$ is given in the article you link to: "The constant k is a simple monochrome bitmap image of the formula treated as a binary number and multiplied by 17. If k is divided by 17, the least significant bit encodes the top right corner; the 17 least significant bits encode the rightmost column of pixels; the next 17 least significant bits encode the 2nd rightmost column, and so on." Just take the image you want, express it in binary, and you have $k$.