Romanesco Broccoli
You may have passed by romanesco broccoli in the grocery store and assumed,
because of its unusual appearance, that it was some type of genetically
modified food. But it’s actually just one of the many instances of fractal
symmetry in nature—albeit a striking one.
In geometry, a fractal
is a complex pattern where each part of a thing has the same geometric pattern
as the whole. So with romanseco broccoli, each floret presents the same
logarithmic spiral as the whole head (just miniaturized). Essentially, the
entire veggie is one big spiral composed of smaller, cone-like buds that are
also mini-spirals.
Incidentally,
romanesco is related to both broccoli and cauliflower; although its taste and
consistency are more similar to cauliflower. It’s also rich in carotenoids and
vitamins C and K, which means that it makes both a healthy and mathematically
beautiful addition to our meals.
Honeycomb
Not only are bees
stellar honey producers—it seems they also have a knack for geometry. For thousands of years, humans have
marveled at the perfect hexagonal figures in honeycombs and wondered how bees
can instinctively create a shape humans can only reproduce with a ruler and
compass. The honeycomb is a case of wallpaper symmetry, where a repeated
pattern covers a plane (e.g. a tiled floor or a mosaic).
How and why do bees
have a hankering for hexagons? Well, mathematicians believe that it is the perfect shape to allow bees to store
the largest possible amount of honey while using the least amount of wax. Other
shapes, like circles for instance, would leave a gap between the cells since
they don’t fit together exactly.
Other observers, who
have less faith in the ingenuity of bees, think the hexagons form by
“accident.” In other words, the bees simply make circular cells and the wax
naturally collapses into the form of a hexagon. Either way, it’s all a product
of nature —and it’s pretty darn impressive.
Sunflowers
Sunflowers boast
radial symmetry and an interesting type of numerical symmetry known as the Fibonacci
sequence. The Fibonacci sequence is 1, 2, 3, 5, 8, 13, 21, 24, 55,
89, 144, and so on (each number is determined by adding the two preceding
numbers together).
If we took the time to
count the number of seed spirals in a sunflower, we’d find that the amount of
spirals adds up to a Fibonacci number. In fact, a great many plants (including
romanesco broccoli) produce petals, leaves, and seeds in the Fibonacci
sequence, which is why it’s so hard to find a four-leaf clover.
Counting spirals on
sunflowers can be difficult, so if you want to test this principle yourself,
try counting the spirals on bigger things like pinecones, pineapples, and
artichokes.
But why do sunflowers
and other plants abide by
mathematical rules? Like the hexagonal patterns in a beehive, it’s
all a matter of efficiency. For the sake of not getting too technical, suffice
it to say that a sunflower can pack in the most seeds if each seed is separated
by an angle that’s an irrational number.
As it turns out, the
most irrational number is something known as the golden ratio, or Phi, and it
just so happens that if we divide any Fibonacci or Lucas number by the
preceding number in the sequence we get a number close to Phi (1.618033988749895
. . .) So, for any plant following the Fibonacci sequence, there should be an
angle that corresponds to Phi (the “golden angle”) between each seed, leaf,
petal, or branch.
Nautilus Shell
In addition to plants,
some animals, like the nautilus, exhibit Fibonacci numbers. For instance, the shell of a nautilus is grown in a “Fibonacci spiral.” The spiral occurs because of
the shell’s attempt to maintain the same proportional shape as it grows
outward. In the case of the nautilus, this growth pattern allows it to maintain
the same shape throughout its whole life (unlike humans, whose bodies change
proportion as they age).
As is often the case,
there are exceptions to the rule—so not every nautilus shell makes a Fibonacci
spiral. But they all adhere to some type of logarithmic spiral. And before you
start thinking that these cephalopods could have kicked your butt in math
class, remember that they’re not consciously aware of how their shells are
growing, and are simply benefiting from an evolutionary design that lets the
mollusk grow without changing shape.
Animals
Most animals have bilateral symmetry—which means that they can be split into two
matching halves, if they are evenly divided down a center line. Even humans
possess bilateral symmetry, and some scientists believe that a person’s
symmetry is the most important factor in whether we find them physically
beautiful or not. In other words, if you have a lopsided face, you’d better
hope you have a lot of other redeeming qualities.
One animal might be
considered to have taken the whole symmetry-to-attract-a-mate thing too far;
and that animal is the peacock. Darwin was positively peeved with the bird, and
wrote in an 1860 letter that “The sight of a feather in a peacock’s tail,
whenever I gaze at it, makes me sick!”
To Darwin, the tail
seemed burdensome and didn’t make evolutionary sense since it didn’t fit his
“survival of the fittest” theory. He remained furious until he came up with the
theory of sexual selection, which asserts that animals develop certain
features to increase their chances of mating. Apparently peacocks have the
sexual selection thing down pat, since they are sporting a variety of
adaptations to attract the ladies, including bright colors, a large size, and
symmetry in their body shape and in the repeated patterns of their feathers.
Spider Webs
There are around 5,000
types of orb web spiders, and all create nearly perfect circular webs with almost equidistant radial supports coming out of the middle
and a spiral woven to catch prey. Scientists aren’t entirely sure why orb
spiders are so geometry inclined since tests have shown that orbed webs don’t
ensnare food any better than irregularly shaped webs.
Some scientists
theorize that the orb webs are built for strength, and the radial symmetry helps to evenly
distribute the force of impact when prey hits the web, resulting in less rips
in the thread. But the question remains: if it really is a better web design,
then why aren’t all spiders utilizing it? Some non-orb spiders seem to have the
capacity, and just don’t seem to be bothered.
For instance, a
recently discovered spider in Peru constructs the individual pieces of its web
in exactly the same size and length (proving its ability to “measure”), but
then it just slaps all these evenly sized pieces into a haphazard web with no
regularity in shape. Do these Peruvian spiders know something the orb spiders
don’t, or have they not discovered the value in symmetry?
Crop Circles
Give a couple of
hoaxers a board, some string, and the cloak of darkness, and it turns out that
people are pretty good at making symmetrical shapes too. In fact, it’s because
of crop circles’ incredible symmetries and complexities of design that, even
after human crop-circle-makers have come forward and demonstrated their skills,
many people still believe only space aliens are capable of such a feat.
It’s possible that
there has been a mixture of human and alien-made crop circles on earth—yet one
of the biggest hints that they are all man-made is that they’re getting
progressively more complicated. It’s counter-intuitive to think that aliens
would make their messages more difficult to decipher, when we didn’t even
understand the first ones. It’s a bit more likely that people are learning from
each other through example, and progressively making their circles more
involved.
No matter where they
come from, crop circles are cool to look at, mainly because they’re so geometrically impressive. Physicist Richard Taylor did a study
on crop circles and discovered—in addition to the fact that about one is
created on earth per night—that most designs display a wide variety of symmetry
and mathematical patterns, including fractals and Fibonacci spirals.
Snowflakes
Even something as tiny
as a snowflake is governed by the laws of order, as most snowflakes exhibit
six-fold radial symmetry with elaborate, identical patterns on each of its
arms. Understanding why plants and animals opt for symmetry is hard enough to
wrap our brains around, but inanimate objects—how on earth did they figure
anything out?
Apparently, it all boils down to chemistry; and specifically, how water
molecules arrange themselves as they solidify (crystallize). Water molecules
change to a solid state by forming weak hydrogen bonds with each other. These
bonds align in an ordered arrangement that maximizes attractive forces and
reduces repulsive ones, which happens to form the overall hexagonal shape of the snowflake. But as
we’re all aware, no two snowflakes are alike—so how is it that a snowflake is
completely symmetrical with itself, while not matching any other snowflake?
Well, as each
snowflake makes its descent from the sky it experiences unique atmospheric
conditions, like humidity and temperature, which effect how the crystals on the
flake “grow.” All the arms of the flake go through the same conditions and
consequently crystallize in the same way – each arm an exact copy of the other.
No snowflake has the exact same experience coming down and therefore they all
look slightly different from one another.
Milky Way Galaxy
As we’ve seen,
symmetry and mathematical patterns exist almost everywhere we look—but are
these laws of nature limited to our planet alone? Apparently not. Having
recently discovered a new section on the edges of the Milky Way Galaxy,
astronomers now believe that the galaxy is a near-perfect mirror image of itself. Based on this new information, scientists are more
confident in their theory that the galaxy has only two major arms: the Perseus
and the Scutum-Centaurus.
In addition to having mirror symmetry, the Milky Way has another incredible
design—similar to nautilus shells and sunflowers—whereby each “arm” of the
galaxy represents a logarithmic spiral beginning at the center of the galaxy
and expanding outwards.
Sun-Moon Symmetry
With the sun having a
diameter of 1.4 million kilometers and the Moon having a diameter of a mere
3,474 kilometers, it seems almost impossible that the moon is able to block the
sun’s light and give us around five solar eclipses every two years.
How does it happen?
Coincidentally, while the sun’s width is about four hundred times larger than
that of the moon, the sun is also about four hundred times further away. The symmetry in this ratio makes the sun and the moon appear almost the same size when seen
from Earth, and therefore makes it possible for the moon to block the sun when
the two are aligned.
Of course, the Earth’s
distance from the sun can increase during its orbit—and when an eclipse occurs
during this time, we see an annular, or ring, eclipse, because the sun isn’t
entirely concealed. But every one to two years, everything is in precise
alignment, and we can witness the spectacular event known as a total solar eclipse.
Astronomers aren’t
sure how common this symmetry is between other planets, suns, and moons, but
they think it’s pretty rare. Even so, we shouldn’t suppose we’re particularly
special, since it all seems to be a matter of chance. For instance, every year
the moon drifts around four centimeters further away from Earth, which means
that billions of years ago, every solar eclipse would have been a total
eclipse.
If things keep going
the way they are, total eclipses will eventually disappear, and this will even
be followed by the disappearance of annular eclipses (if the planet lasts that
long). So it appears that we’re simply in the right place at the right time to
witness this phenomenon. Or are we? Some theorize that this sun-moon symmetry
is the special factor which makes our life on Earth possible.
