Fractal Geometry:
Fractals have played a large part in the modernist literary
tradition, especially on the stage. A
play within a play is the most common literary denominator of the fractal
method. With an understanding that
integers are numbers that have no decimal expansion (i.e. whole and real
numbers), fractals in geometry employ non-integer numbers, creating expansive
sets of algorithms as they have few limitations. Essentially, this means that fractal images
are between one and two dimensional. As
fractals are geometrically manifest, they form discernable patterns. In order to create the pleasant fractal
images that modern art has championed, color is added where changes of pattern
occur, creating symmetrical distinctions pleasant to the human eye. Any minimized or maximized view of a fractal
should be undistinguishable in their raw form.
Literary tradition uses the fractal method to create mirroring in plot
and characters, especially where the dimension of time is the background the
patterns are spread across. Additionally, fractals can be found in nature and
create some of the most pleasing art.
Fractals in Arcadia :
When faced with the limitations of traditional geometry,
Thomasina looks to the fractals of nature in veins of a leaf in order to
stumble on to her iterated algorithms.
Her abject frustration is most famously shown as she speaks to her
tutor:
"Each week I plot your equations dot for dot, x's
against y's in all manner of algebraical relation, and every week they
draw themselves as commonplace geometry, as if the world of forms were nothing
but arcs and angles. God's truth, Septimus, if there is an equation for a bell,
then there must be an equation for a bluebell, and if a bluebell, why not a
rose?"
Thomasina’s break from traditional methods is a meta-manifestation
of the post-modernist movement and its breaking with traditional
knowledge. The impact of this science
has a profound effect on the intellectual characters and fractals become a very
integral part of the plot— but is the dichotomy of stories within the play a
fractal itself? There are certainly
similarities between the questioning characters Thomasina and Chloe, or Gus and
Augustus and their hobbies. However,
with the obvious differences in time and characteristics between these pairs,
can we really say that the stories follow the same fractal pattern?
For more on the mathematics in arcadia:
http://www.youtube.com/watch?v=iM0cR7qvmgY&noredirect=1
-Christian Sorensen
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