# I want to draw a fractal, logically!

I want to draw a fractal, logically.

It's not a fib, I assure you (well maybe...).

If you have a plan,

Then you're the man (or woman)!

Hint 1 (a small one):

There may be abbreviations, don't take the capitalization too literally, and things can have multiple meanings.

Hint 2 (small spoiler):

I'm looking for an algorithm.

Hint 3 (big spoiler!!):

It should use Boolean values.

Did I fib or not?

Fib refers to the Fibonacci series, which can be used to draw a Sierpinski triangle, the fractal I want to draw. The desired approach is somewhat different of course--it must be logical--but it's related.

• Are you sure this is tagged correctly? It looks to me like this needs the riddle tag (and possibly enigmatic-puzzle as well). Jun 28 '18 at 15:13
• No problem! The rhyme tag may be applicable as well, as it looks like this is intended to be a limerick. Jun 28 '18 at 15:20
• @F1Krazy It's not a limerick, and in fact doesn't even rhyme. Jun 28 '18 at 15:21
• I think it means "Fib" and not "fib". Proper nouns start with a capital letter. This might be a snowflake or sponge of a question. :P Jun 28 '18 at 15:23
• Well, it could be "fib" as in "minor lie". Though it wouldn't be astonishing if it were "Fib", short for Fibonacci... Jun 28 '18 at 15:29

There's a really neat way to draw a famous fractal, namely the

using elementary logic only:

Step 1: take the numbers from $0$ to $2^n-1$ in two dimensions, use them as coordinates

Step 2: plot a 3D column graph, where the height of each bar is

the bitwise NAND of the coordinate numbers at that point.

Here's what it looks like for n=4

• that's cool...please tell me what it has to do with the original riddle?
– Dr t
Jun 28 '18 at 16:35
• @Drt Well, the riddle asks to draw a fractal logically, it is named after a man, fibonacci has nothing to do with it, and it fits the hints 2 and 3 extremely well. So... quite a lot, actually?
– Bass
Jun 28 '18 at 16:37
• I think the line about "man or woman" in the riddle is a reference to (ROT13) "gur traqre ovanel". Jun 28 '18 at 16:39
• Fibonacci comes into play; see the spoiler tag in the update for an explanation.
– bob
Jun 28 '18 at 16:46
• Awesome job bass! I really like the graphic too.
– bob
Jun 28 '18 at 16:48

Well, while an image can follow later, consider this:

Construct a right angled triangle with sides as 1,1. This gives a diagonal of size square root(2). Then form another right angled triangle, whose sides are the diagonal of the previous construction and 1, which results in a diagonal of size square root(3) and so on.

Then, joining

the 'rotating' points of such a construction results in a spiral, leading later to a fractal.

• That sounds interesting--I'd love to see the diagram. You've got part of the idea but as a hint I'll point you back to the word "logically".
– bob
Jun 28 '18 at 16:49