Photo: Tim Garrett
and Cale Fallgatter
Until now, photographs of snowflakes have been
beautiful images of two-dimensional single
flakes. However, the majority of snow falls in
clumps. Recently, Tim Garrett and a team in Utah
developed a camera system called the MultiAngle Snowflake Camera, capable of capturing
images of snowflakes in 3D as they fall from the
sky. Three high-speed cameras are triggered
by infrared sensors and use extremely fast
exposures (up to 1/2,500th of a second) to
photograph snowflakes and monitor their path
and speed as they fall. 3D imagery is helping to
create a better understanding of snowcrystals
and snowfall and shows us that our traditional
imagining of six-sided flakes falling from the
sky needs some updating!
https://www.youtube.com/watch?v=iOfkukhb1Os
Fractals and Snowflakes
Go to any sing-along “Frozen” performance and
you’ll hear 3-year-olds belting out the line “My
soul is spiralling in frozen fractals all around”
from “Let it Go”. Snowflakes don’t develop using
the algorithms of fractal repetition, so what is
the relationship between fractals and snow?
Snow crystals begin as either a single ice
crystal or an aggregation of ice crystals falling
through high-humidity cold air. As the crystal
falls it rotates, and the snowflake grows at its
perimeter. Complex shapes emerge as the flake
moves through different temperatures and
humidity, creating individual snowflakes that
are nearly unique in structure at the molecular
level. Many snowflakes form structures that
lack symmetry and therefore aren’t fractals.
However, fractal geometry has long been
associated with snowflakes as the patterns
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fractals create approximate real snowflakes
very closely, and it is fractal mathematics which
is of most use in the analysis of snowflake
structures.
The Swedish mathematician Helge von
Koch (1870-1924) formulated one of the first
mathematical fractals now known as the Koch
snowflake. In it you start with an equilateral
triangle, then with each iteration remove the
middle third of each side and add two line
segments to make new equilateral triangles on
each side of the previous triangle, this builds up
the snowflake shape. If you zoom into the edge
of the snowflake you won’t be able to tell how
many iterations have been performed. Infinite
repetition of the iteration equals a snowflake
with an infinite perimeter, even though the
snowflake itself only has a finite area.