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One day I thought suddenly of the fractal snowflake. Prior to that
I had been reading the Bible, and I did not know why I had thought of
the fractal snowflake until I drew it.
The fractal snowflake is created in the following manner. Draw an
equilateral triangle. Separate each of its sides into three equal
components, and in the middle of each create an equilateral triangle
whose sides are equal to that middle component. Keep repeating the
process with every component triangle. Here, due to formatting
restrictions, I have shown the fractal snowflake as it exists at the
third level. The constant lines represent the sides of each triangle;
the dashed lines (ones with spaces between the lines) serve another
purpose, which will be revealed later.
The concept of fractals has been used in the holographic theory of the
Universe: That the same pattern exists and replicates at all levels of
structure, and that in any part of the universe can be observed its
laws that therefore contain the key to the whole.
Besides that, however, I discovered something more interesting: That
if I drew through the snowflake lines that are an extension of each
side of each component triangle, it connected to a side of another
triangle on the other side of the snowflake. This led me to conclude
that there is another aspect to the interconnectedness: That everything
was balanced against its opposite and could trace its reflection to
another side. It is also worth mentioning that each connecting line
connected the triangle to another triangle at the same level of
structure, with the second set of triangles (second level) connecting
to other members of the second level triangles, and with the third
set of triangles containing connections to members of the third set.
(In this drawing, the lines between second-level triangles are shown
as dashed lines; the lines between third-level triangles are omitted
for formatting reasons, with the exception of the top set of triangles
with the triangles on opposite sides to whose sides they connect -
likewise shown as dashed lines).
Similarly (not shown here), a line drawn from the corner of each
component triangle bissecting the triangle came out on the other side
of the snowflake bissecting another component triangle, likewise at
the same level of structure.
Now for the really exciting stuff. The imaginary lines (shown in
dashes) drawn as extensions of the sides of the component triangles,
both on second level and in the case of the top triangle, all created
David's stars. This likewise can be observed at every level of
structure by tracing the intersection of lines composing the triangles
and imaginary lines drawn through the snowflake connecting the sides of
the triangles to their opposites. The Star of David has of course been
used as a metaphor for God's workings - and here in fractal snowflake
we see God manifest at every level, from the most overarching to the
most detailed.
In C. S. Lewis's _Screwtape_Letters_, divine love is seen to be the
all-pervading force that connects all to all and all to God. The Holy
Trinity is seen to be the glue holding the world together. Here, we
see the Holy Trinity manifest at each level of manifestation, from the
top to the bottom, and to live and top and manifest at all levels.
My high school mathematics teacher, who is a Christian, says that there
is no conflict between mathematics and Christianity. And here we have a
mathematical entity that appears to model God's working - while also
incor****ating the holistic theory that has motivated New Age beliefs -
and integrate it into Christian theological thought.
This, indeed, creates a unison between mathematics, holistic theory
and Christianity. And reconciles the pieces, like component sets of
triangles, into the integrated whole.
Ilya Shambat.
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