Dho-Na Curve of the Sleeper

One of Charles Stross's more intriguing scenery details* in his Laundry novels is the idea of a Dho-Na curve (which sounds beautifully like 'Do-Not').
A Dho-Na curve is a modern elaboration on several ideas of magical geometry, and while its clear that there are several subsets of the Curve, some of them discovered in the far past (Alhazred,738), but most of them
computationally discovered.If they are iteratively or formulaicly derived is an exercise left to the readers imagination, but we can make some inferences.

In Stross's 1940's, German necromancers were calculating subsets of the Curve using Konrad Zuse's stolen Z-1 mechanical computer. This was a rather sophisticated machine, capable of 22-bit operations on a 64 -bit register. The interesting thing about it was that it ran the program as it read it off of punched tape, and printed its output as it went. Stross dictates supernatural penalties for complex computation/cogitation, but I suspect that the Z1, by the very natural of its one-step RAM-less processor  was quite immune to possession by creatures from the Dungeon Dimensions.

I digress.
To a mathematician, a curve is not necessary smooth and curvy, the Koch Snowflake being my favorite holotype.
In the spirit of the old 'ABRACADBRA' magic squares**, or the Sator Square, I started tinkering with this rule:

10      Write the letter of the seed.
20      Write up to three copies of the next letter of the seed, in any of the four cardinal directions,
                   EXCEPT   when it would touch an already written letter( diagonal contacts are permitted).
30      GOTO 20***

Using the Phrase of the Sleeper ( I was originally doodling the line 'Oak Island Treasure' ) generates this:



Note that it generates  the seed phrase minus its first letter reversed twice, along with astounding babble like
"ng  ag ngat  htagn hf uf hfuh lhuf ngn hfh lu hu fuf gag ngathfuhluht"
Sprinkle that with apostrophes and bake for 30 minutes at 350, and you've got a sentence worthy of any Dagonian!

"Ia! Ia! Cthuhlu f'thagn! Ng'ag ngat  htagn 'hf!  Uf'hfuh lhuf ngn! Hfh lu hu fuf gag ngathfuhluht!"

Of course, we only have a scrap of a phrase, which limits the size we can inscribe.
We could of course, generate a 'Cthulhu Fh'tagn ' modified Thue-Morse sequence which may be awesomely cool.

What else?
Once the sentence is complete,  every letter could be replaced with a smaller version of the whole curve, starting a Koch Curvature.

The textual plane could be rotated , and a Cthulhubulb**** generated.


All single letter words could be struck out, opening the lacework pattern.



...I managed to get three possessive apostrophes into one sentence in this post, which I think is a personal record.


* Atrocity Archive, for instance. Read it. Its the best of the set.

** Although the first example in literature is a triangle.(Quintus Serenus Sammonicus,Liber Medicinalis, 3BC)

*** "GOTO is a bad command"...yeah whatever, bite me.
****From which we hatch a Baal-zehulubulbette.

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