PATTERNS IN NATURE
AND THE WORLD
Mathematics in the Modern World by Abelita V. Lubrica
OBJECTIVES OF THE LESSON:
At the end of the lesson, you should be able to:
1. be aware of the different patterns that can be found in
nature,
2. realize the different uses of each pattern,
3. make an interconnection between the patterns and
mathematics, and
4. appreciate math and its relationship to the environment.
WHAT IS A PATTERN?
• a repeated decorative design (Oxford Dictionary)
• a natural or chance configuration (Merriam-Webster)
• a reliable sample of traits, acts, tendencies, or other observable
characteristics of a person, group, or institution (MerriamWebster)
• synonyms:
design, decoration, motif, marking, ornament, ornamentation,
device, figure
WHAT ARE THE KINDS OF PATTERNS
FOUND IN NATURE?
1. SYMMETRY – the quality of being made up of exactly similar parts
facing each other or around an axis (Oxford Dictionaries)
• Kinds of symmetry :
1. reflectional symmetry (mirror or line symmetry) - occurs when
an image can be flipped around an axis and still appear the same
2. rotational symmetry - object remains the same after being
rotated around a central point
3. point symmetry - occurs when every point of an image has a
matching point that is the same distance from the central point but in
the opposite direction
REFLECTIONAL OR LINE SYMMETRY
ROTATIONAL SYMMETRY
ROTATIONAL SYMMETRY
POINT SYMMETRY
RELATIONSHIP OF ROTATIONAL
AND POINT SYMMETRY
USE OF SYMMETRY
*efficient locomotion
*gives balance and beauty
(https://www.cbc.ca/radio/quirks/july-21-2018-bread-came-before-agriculturedriving-drowsiness-and-more-1.4753031/the-reason-why-most-animals-aresymmetrical-has-to-do-with-their-locomotion-1.4753044)
PATTERNS IN NATURE
2. SPIRAL – winding in a continuous and
gradually widening (or tightening)
curve, either around a central point on
a flat plane or about an axis so as to
form a cone
SPIRALS
SPIRALS
Here is a link showing the presence of spirals in nature:
Part 2: Spirals in Nature
https://www.youtube.com/watch?v=ewLFSIyBJkU
Spirals in Nature are the Signature of the Divine Architect, aka Universal
Mind!
https://www.bitchute.com/video/PXUel0sLwo8d/
USE OF SPIRALS
*when the plant is in spiral shape, it condenses itself causing it
to be more compact, stronger, and more protected from the
elements like wind, water, or sunshine
*defenses of animals or plants are more robust or stronger
*more efficient use of resources like water or sunlight
*maximization of space
*gives beauty
https://www.fi.edu/math-patterns-nature
PATTERNS IN NATURE
3. FRACTALS and TREES
• Fractal - any of various extremely irregular curves or shapes
for which any suitably chosen part is similar in shape to a
given larger or smaller part when magnified or reduced to
the same size
- a fractal is a detailed pattern that looks similar at any
scale. The small part is similar in shape and pattern to the big
part and the big part is similar to the small part.
ROMANESCO BROCOLLI
FRACTALS – MANDELBROT SET
FRACTALS- THE SIERPINSKI
TRIANGLE
FRACTALS
• Here is a link showing fractals in nature:
Fractals in Nature
https://www.youtube.com/watch?v=GKYG__-HATI
USE OF FRACTALS
Fractals are hyper-efficient in their construction and
this hyper-efficiency:
*makes plants maximize their exposure to sunlight
* paves efficient transport of nutrition throughout the
cellular structure of living things
• (https://www.diygenius.com › fractals-in-nature)
USE OF FRACTALS:
• fractal patterns of growth have a mathematical, as well as
physical, beauty.
• fractals are also used in computer graphics, data
compression, and modeling complex systems.
PATTERNS IN NATURE
4. Flow and meanders
• Flow – move along or out steadily and
continuously in a current or stream
• Meander – follow a winding course
MEANDER
MEANDERS
USE OF MEANDERS
As the river bends and turns
*the river path (channel) gradient is reduced
*makes the water less erosive thus, also,
equilibrium is maintained
• (https://www.ausableriver.org/blog/why-do-streamsmeander)
USE OF FLOW AND MEANDER
PATTERNS
• Understanding flow and meander patterns is crucial for
predicting and managing floods or flood control and it is
also useful for water supply management.
PATTERNS IN NATURE
5. Waves and Dunes
• Wave – a long body of water curling into an arched
form and breaking on the shore
• Dune – a mound or ridge of sand or other loose
sediment formed by the wind, especially on the sea
coast or in a dessert
USE OF WAVES
• Waves are a very important and necessary part of the
functioning of the Earth.
• The motions they create perform a vital role in (1)transporting
energy around the globe and (2) shaping the coastlines.
• Ocean waves, particularly long-travelled swells, are a very
important element in the complex web of mechanisms that
control the heat balance of the planet.
(http://www.surf-science.org/articles/the-importance-of-waves)
USE OF WAVES
• Waves possess kinetic energy that can be harnessed and
converted into electricity through wave energy converters.
It is an example of a source of renewable energy.
USE OF DUNES
• Natural sand dunes play a vital role in
• (1)protecting our beaches, coastline and coastal
developments from coastal hazards such as erosion,
coastal flooding and storm damage.
• They provide (2) shelter from the wind and sea spray
to man, animals and plants.
• (3) provide a future supply of sand to maintain the
beach.
PATTERNS IN NATURE
6. Bubbles and Foam
• Bubble – a thin sphere of liquid enclosing air or
another gas
• Foam – a mass of small bubbles formed on or
in liquid typically by agitation or fermentation
Bubbles, foam
USE OF BUBBLES AND FOAM
• In the oceans, bubbles have a useful role by helping
to convert salt into an aerosol, a crucial step in
creating clouds.
• The purpose of foam is to provide contact time on a
soiled surface to allow the wetting agents,
detergents and degreasers enough time to clean or
remove dirt and grease.
(How the bubble bursts | Naturehttps://www.nature.com)
(https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjz5p739tP1AhWLMpQKHfcdCnkQFnoECAkQAw&url=https%3A%2F%2F
cleanersolutions.net%2Fwhat-you-need-to-know-about-foam%2F&usg=AOvVaw3oK3d9yxZVZI8GgZjZqZCa
USE OF BUBBLES
• bubbles are also a useful survival tool, they improve hunting success
or breathing underwater.
• Fishes create bubble nests to house their eggs until they hatch
• shrimps use bubbles to catch their prey.
• Crabs blow bubbles to keep their gills moist.
• Beluga whales blow bubbles underwater and express their moods
with the different shapes of their bubbles.
• For snails, blowing bubbles is a way to protect themselves.
OTHER USE OF BUBBLES AND
FOAM
• Bubbles have very important applications in
many fields such as shipbuilding engineering,
ocean engineering, mechanical engineering,
environmental engineering, chemical
engineering, medical science and other fields.
• Foam is widely employed for insulation, packaging,
cushioning, safety.
• Give beauty
PATTERNS IN NATURE
7. Tessellations
tessellate – decorate or cover a surface
with a pattern of repeated shapes,
especially polygons, that fit together
closely without gaps or overlapping
AN EXAMPLE OF TESSELLATION (ALSO
VORONOI BY BEES)
Why do honeybees love hexagons? - Zack Patterson and Andy Peterson
• https://www.youtube.com/watch?v=QEzlsjAqADA
USE OF TESSELLATIONS
•gives beauty
•efficiency in the use of space and
materials like the beeswax
8. Cracks
crack - break or cause to break
without a complete separation of the parts
USE OF CRACKS
• Cracks are linear openings that form in materials to
relieve stress. When a material fails in all directions it
results in cracks.
• (https://heathercline.zenfolio.com)
USES OF CRACKS
• Cracks patterns can give a valuable insights into the
structural integrity of a building and other infrastructures.
Understanding crack patterns can help in improving design,
ensuring safety and maintaining long-term functionality of
infrastructures.
• indicate material failure
PATTERNS IN NATURE
9. Spots and Stripes
• Spot - a small round or roundish mark,
differing in color or texture from the
surface around it
• Stripe– a long band or strip differing in
color or texture from the surface on either
side of it
USE OF SPOTS AND STRIPES
• attracting mates
• camouflage
• mechanism as the heat-absorbing black
stripes become hotter than the reflective
white one's, creating temperaturelowering strips
FOOTNOTE ON THE USE OF SPOTS
AND STRIPES
• Another function of a zebra's stripes is too ward off biting
flies that can carry deadly diseases. The wavy lines of a
zebra blend in with the wavy lines of the tall grass around it.
• The color of the stripes does not matter because the main
predator of the zebra, the lion, is color blind. The stripes
enable the zebra to blend in with the grass and it
surroundings.
PATTERNS IN NATURE
10. VORONOI
In a Voronoi pattern, every point within a given region is
closer to the “seed” inside that region than it is to any other point
outside that region.
Each point along a region's edge is equidistant from the two
nearest seeds.
It's seen in places ranging from cracked mud to giraffe skin to
foamy bubbles.
https://www.msichicago.org › exhibits › the-patterns ›
PATTERNS IN NATURE
A Voronoi pattern shows the proclivity of nature to
favor efficiency such as
a. the nearest neighbor,
b. the shortest path,
c. the tightest fit and
d. the maximization of resources.
•Examples of Voronoi patterns are
the skin of a giraffe, corn on the
cob, honeycombs, foam bubbles,
the cells in a leaf, and the head of
garlic
• Voronoi patterns optimize the distribution of resources such
as water, nutrients, and light, as well as maximize the
efficient use of available space.
• These patterns ensure that each element in a system has
access to necessary resources while minimizing wastage.
THE HONEYCOMB AND URBAN
PLANNING AND VORONOI
• The honeycomb structure, often found in beehives, exemplifies the Voronoi
pattern. Bees construct hexagonal cells that fit together seamlessly, creating
a tessellated arrangement. This pattern maximizes the use of space within
the hive while providing efficient storage for honey and eggs. Each cell
shares walls with adjacent cells, enabling efficient temperature regulation
and storage capacity.
The Voronoi pattern finds applications in urban planning through its ability to
optimize resource distribution, analyze spatial relationships, and guide the
layout of infrastructure and services within cities.
USE OF VORONOI
•efficiency in the distribution of water,
nutrients and light
•efficient use of space
•optimization or maximization of the
use of resources
•beauty
Nature by Numbers by Cristobal Vila
https://www.youtube.com/watch?v=kkGeOWYOFoA
“I hope that the discussion
regarding the patterns that can
be seen in nature added to your
knowledge.” AV Lubrica