Thursday 30 April 2015

Not really self-referential; still cool though

I was inspired when reading about Tupper's self-referential formula to derive my own version of such a formula. The formula looks impressive but isn't really too difficult to understand or derive from scratch. (And it isn't really self-referential either as it creates all possible bitmaps. The trick is just in figuring out how to find the right region of the graph that contains your bitmap.)

So I wanted to do a simple 10x10 bitmap containing an image of "Hi!". After a bit of work on paper I got to this inequality, where w and h are the width and height of the region respectively:

It's a bit better than Tupper's one because it plots things uninverted, i.e. the way you'd expect them to be

So, after creating a quick Python script to calculate k, the starting y-coordinate on the graph, which is a massive 6165710764903459078666956800 (for my formula only, not Tupper's original one), I got this plot:

Hooray!

1 comment:

  1. If anybody can describe to me what the bitmap in the region y in [k+10, k+20] looks like and x in [0, 10], I'll buy you a drink.

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