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This is a list from my website of the trefoils and hexagrams that can be derived from the first few numerical triangles, by one iteration of the Koch snowflake and Koch antisnowflake processes.

Pixellated triangles can only approximate to Koch snowflakes/antisnowflakes, but they are all produced by ...

Great work Bill! Do you draw those Koch Snowflake iterations by hand or programmatically?


I do them by hand. I like to roll my sleeves up and get digging, rather than rely on programming.


You are correct it is T(112) but that's really the 38th "generating triangle" in the sense that only ...

I showed how the very name of Jesus Christ in Greek points to both Genesis 1:1 and John 1:1 as prime/semiprime pointers (note that semiprimes require 1 to be excluded from the primes, or else all primes, by definition, would have to be counted among the semiprimes):

"Jesus Christ" (SG) = 2368 ...

The beforegoing verse Exodus 3:1 had "achar hamidbar"
https://www.sefaria.org/Exodus.3.1?ven=english|The_Five_Books_of_Moses,_by_Everett_Fox._New_York,_Schocken_Books,_1995&lang=bi&aliyot=0
He led the flock behind the desert ("achar hamidbar")
and came to the mountain of God, to Horeb.

"midbar ...

The Koch snowflake iterates we've been discussing connect T37 to T112, and through that connection, Genesis 1.1 to John 1.1, and in three ways. Here is Richard's table again, showing the iterates arising from the first few stars.


RAM Table.png


The second iteration of hexagram 937 is snowflake ...

733 is gematria of "labbat-esh" in Exodus 3:2
וַיֵּרָ֠א מַלְאַ֨ךְ יְהֹוָ֥ה אֵלָ֛יו בְּ לַבַּת־אֵ֖שׁ מִתּ֣וֹךְ הַסְּנֶ֑ה וַיַּ֗רְא וְהִנֵּ֤ה הַסְּנֶה֙ בֹּעֵ֣ר בָּאֵ֔שׁ וְהַסְּנֶ֖ה אֵינֶ֥נּוּ אֻכָּֽל

When I found that I thought it to be amazing, since 733 = (7 x 73) + (6 x 37)


It would help if ...

Fermat found that any prime leaving a remainder of 1 when divided by four is the sum of two squares, because all sums of two squares leave a remainder of 0, 1 or 2 mod 4, and for odd primes only 1 is possible.

All of the star and snowflake primes we’ve been discussing - 13, 37, 73, 337, 373, 733 ...

Here are some images that map out the geometry, including mirrored pairs of fractal precursors, created by the joining of Genesis 1.1 and John 1.1.

CS1.png

CS2.png

The next two images show the Koch snowflake and trefoils encoded over the first four and last four natural divisions within the ...

The main rule of prime numbers is that a prime can only be divided by and itself.
Therefore in a straight logical sense, 1 has to be the first prime.
And 1 was the first prime for the most part of human history until the mathematical community decided to change it to number 2 being the first ...

Here is the sequence figurate Koch Snowflake interates:

KS(n,1) = triangular numbers T(n)
KS(n,2) = star numbers S(n)
KS(n,3) = first iterate that looks like a Koch Snowflake = 7KS(n,2) + 6HS(n,2) <<< Made from combo of previous KS(n,2)/HS(n,2)
KS(n,4) = second iterate that looks more like a ...