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MATH Video Summarize - .dcsfgh

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College Algebra with Applications (MATH 124)

35 Documents
Students shared 35 documents in this course
Academic year: 2018/2019
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Niell Quiocson
West Virginia University
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The Mathematics of Biological Patterns

The living world is full of a diverse array of shapes and patterns, from the spots on a

cheetah to the stripes on a zebra. Beneath this stunning variety lies a fundamental

mystery: how do such complex and varied patterns arise from the same simple

building blocks of life - cells and their chemical instructions?

The Genius of Alan Turing

 Alan Turing, a famous mathematician and codebreaker, was fascinated by

the patterns found in biology

 In 1952, Turing published a groundbreaking paper that described a set of

simple mathematical rules that could explain the emergence of many natural

patterns

 These "Turing patterns" range from stripes and spots to labyrinth-like waves

and geometric mosaics

 Turing's work on biological patterns was largely ignored at the time,

overshadowed by other major discoveries in biology

The Power of Reaction-Diffusion

 Turing's key insight was to combine the processes of diffusion (the

spreading out of chemicals) and reaction (the interaction between

chemicals)

 Diffusion alone does not create patterns, it just leads to an even distribution

(like ink in water)

 Simple chemical reactions also do not create patterns, they just convert

reactants into products

 But when diffusion and reaction are combined in a "reaction-diffusion

system", it can lead to the spontaneous formation of complex patterns

"Everybody thought back then that if you introduce diffusion into systems, it would

stabilize it. And that would basically make it boring. What I mean by that is you

wouldn't see a lovely pattern. You'd have an animal, just one color, but actually

Turing showed that when you introduce diffusion into these reacting chemical

systems, it can destabilize and form these amazing patterns." - Natasha Ellison

 This activator-inhibitor model can explain patterns like the spots on a cheetah

or the stripes on a zebra

 Adjusting the parameters in the equations, like the relative rates of diffusion

and reaction, can produce a wide variety of different patterns

Proving Turing Right

 For decades, Turing's mathematical model remained just that - a model.

Biologists needed to find the actual "morphogens" (chemicals/proteins) that

behave according to Turing's predictions

 Recently, biologists have begun to identify real-world molecular mechanisms

that match Turing's reaction-diffusion framework

 Examples include the ridges on a mouse's mouth, the spacing of bird

feathers, and the tooth-like scales of sharks

 However, some biological patterns are more complex, involving the

interaction of multiple activator/inhibitor signals, like the pattern of fingers in

mammalian limbs

The Tragic Fate of a Genius

 Sadly, Alan Turing never lived to see the full impact of his work recognized

 In 1952, the same year he published his groundbreaking paper on biological

patterns, Turing was convicted of "gross indecency" for his homosexuality

and underwent chemical castration

 Two years later, at the age of 41, Turing died from cyanide poisoning, likely a

suicide

 Turing's work was largely ignored for decades, but is now recognized as a

singular achievement, blending mathematics, biology, and computer science

in a way that has transformed our understanding of the natural world

The Unrealized Potential of Alan Turing

 Turing's mathematical insights were so far ahead of their time that he often

struggled to communicate them to others

 Without the powerful computers we have today, Turing had to develop his

own coded system to describe the complex equations underlying his reaction-

diffusion models

 The full extent of what Turing could have achieved if he had lived is

impossible to know, but it is clear that the world lost an extraordinary mind

 Turing's work during WWII as a codebreaker was estimated to have shortened

the war in Europe by over 2 years, saving millions of lives

 After the war, Turing was instrumental in developing the core logic of modern

computing, laying the foundation for the technology we use today

 His lifelong fascination with the mathematics of nature has continued to

inspire new discoveries in biology, deepening our understanding of the living

world

 Digital Security: The importance of secure passwords, highlighted by

LastPass, reflects contemporary concerns about personal data protection

in a digital age.

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MATH Video Summarize - .dcsfgh

Course: College Algebra with Applications (MATH 124)

35 Documents
Students shared 35 documents in this course

University: West Virginia University

Was this document helpful?
First Link
The Mathematics of Biological Patterns
The living world is full of a diverse array of shapes and patterns, from the spots on a
cheetah to the stripes on a zebra. Beneath this stunning variety lies a fundamental
mystery: how do such complex and varied patterns arise from the same simple
building blocks of life - cells and their chemical instructions?
The Genius of Alan Turing
Alan Turing, a famous mathematician and codebreaker, was fascinated by
the patterns found in biology
In 1952, Turing published a groundbreaking paper that described a set of
simple mathematical rules that could explain the emergence of many natural
patterns
These "Turing patterns" range from stripes and spots to labyrinth-like waves
and geometric mosaics
Turing's work on biological patterns was largely ignored at the time,
overshadowed by other major discoveries in biology
The Power of Reaction-Diffusion
Turing's key insight was to combine the processes of diffusion (the
spreading out of chemicals) and reaction (the interaction between
chemicals)
Diffusion alone does not create patterns, it just leads to an even distribution
(like ink in water)
Simple chemical reactions also do not create patterns, they just convert
reactants into products
But when diffusion and reaction are combined in a "reaction-diffusion
system", it can lead to the spontaneous formation of complex patterns
"Everybody thought back then that if you introduce diffusion into systems, it would
stabilize it. And that would basically make it boring. What I mean by that is you
wouldn't see a lovely pattern. You'd have an animal, just one color, but actually
Turing showed that when you introduce diffusion into these reacting chemical
systems, it can destabilize and form these amazing patterns." - Natasha Ellison
This activator-inhibitor model can explain patterns like the spots on a cheetah
or the stripes on a zebra
Adjusting the parameters in the equations, like the relative rates of diffusion
and reaction, can produce a wide variety of different patterns

Students also viewed

Related documents