Nature is full of fascinating patterns, from the spots on cows to the stripes on fish and cheetahs. Alan Turing, a pioneer in computer science, suggested that these patterns might be more similar than they seem. He developed a mathematical model to explain how such patterns could form.
Turing’s model involves two substances within an organism: an activator and an inhibitor. The activator encourages the production of both substances, while the inhibitor slows it down. This interaction is similar to a predator-prey relationship. As the activator population grows, it produces more of itself, but this also provides more resources for the inhibitors, which then increase and reduce the activator population.
As both populations grow, their ranges expand. However, inhibitors need more space, so their range expands faster than that of the activators. This results in activators concentrating in a central area, surrounded by inhibitors. When activators dominate, they can trigger changes like pigment production, creating spots of color.
The beauty of Turing’s theory is its adaptability. By adjusting variables like the spreading rates of the substances or the system’s size, a variety of patterns can emerge. For example, starting with slightly more activator than inhibitor can lead to spots. In narrow systems, like a snake’s body, stripes may form. If the activator spreads quickly, it can create labyrinth-like patterns by merging with other patches.
Turing’s model can simulate patterns seen on animals like cows, fish, and giraffes. However, just because the math works doesn’t mean nature follows these exact rules. Scientists are still exploring whether real-life activators and inhibitors create natural patterns.
Some patterns, such as segments in developing fruit flies, are determined by genetic instructions and don’t follow Turing’s model. However, there are examples that align with his ideas. In developing mice, a protein called “sonic hedgehog” inhibits another activator protein, leading to stripe-like structures in the embryo’s mouth and limbs.
Whether or not Turing’s theory perfectly mirrors reality, its greatest contribution may be inspiring biologists to look for evidence of these concepts in nature. This blend of observation and theory helps us understand how patterns like those on cheetahs develop.
This video was supported by Audible, which offers a wide range of audiobooks, including “The Information” by James Gleick. This book delves into how figures like Alan Turing have shaped our understanding of information. To download “The Information” or another book and support MinuteEarth, visit www.audible.com/minuteearth.
Additionally, we previously conducted a survey about personal experiences with asparagus and received many insightful responses. You can find the results linked in the description below.
Engage with a computer simulation that models Turing’s activator-inhibitor system. Adjust parameters like diffusion rates and initial concentrations to observe how different patterns emerge. This hands-on activity will help you visualize the mathematical concepts and understand the dynamics of pattern formation.
Select an animal with distinct patterns, such as a zebra or a leopard. Research how Turing’s model might explain these patterns and present your findings in a short report. This activity will deepen your understanding of the model’s application in real-world scenarios.
Participate in a group discussion to explore the role of genetics and Turing’s model in pattern formation. Debate the extent to which each factor contributes to the development of animal patterns. This will enhance your critical thinking and ability to articulate scientific concepts.
Work through the mathematical derivation of Turing’s equations with your peers. This activity will reinforce your understanding of the mathematical foundation behind the model and improve your problem-solving skills.
Use art supplies or digital tools to create your own patterns based on Turing’s principles. Experiment with different variables to see how they affect the resulting designs. This creative exercise will allow you to apply theoretical knowledge in a fun and imaginative way.
Here’s a sanitized version of the provided YouTube transcript:
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Nature exhibits a seemingly endless array of patterns – from the spots on cows to the stripes on surgeonfish to the patterns on cheetahs. Alan Turing, known for his contributions to computer science, proposed that these patterns might not be as different as they appear. To illustrate his idea, he developed a simple set of mathematical rules that could generate various patterns.
According to Turing’s model, there are two substances within each theoretical organism: an activator and an inhibitor. The activator promotes the production of both substances, while the inhibitor slows it down. This relationship resembles a predator-prey dynamic: as the population of activators increases, they produce more of themselves, but a larger population also means more food for the inhibitors, leading to an increase in their numbers, which in turn reduces the activator population.
Turing’s rules suggest that as the populations of both activators and inhibitors grow, their ranges expand. However, the inhibitors require more space, causing their range to expand more rapidly than that of the activators. Consequently, the activators become concentrated in a central area, surrounded by a region dominated by inhibitors. When the activator is more prevalent than the inhibitor, it can trigger changes, such as the production of pigment, resulting in spots of color.
The beauty of Turing’s theory lies in its flexibility; by adjusting variables like the spreading rates of the activator and inhibitor or the overall area of the system, a wide variety of patterns can emerge. For instance, starting with slightly more activator than inhibitor in certain areas may lead to the formation of spots. In a narrow system, such as a snake or a tail, stripes may develop. If the activator spreads more quickly, it can create labyrinth-like patterns by merging with other patches.
Turing’s rules have the potential to simulate patterns that resemble those found on cows, fish, giraffes, and even the tentacles of hydras. However, the fact that these mathematical rules work theoretically does not confirm that nature operates under the same principles. Decades later, scientists are still investigating whether some natural patterns arise from real-life activators and inhibitors.
On one hand, some patterns, like the segments in developing fruit flies, are predetermined by genetic blueprints and do not follow Turing’s model. On the other hand, there are intriguing examples that align with Turing’s ideas, such as in developing mice, where a protein called “sonic hedgehog” inhibits another activator protein, resulting in stripe-like structures in the embryo’s mouth and limbs.
Regardless of how accurately Turing’s theory reflects the real world, its greatest impact may be its ability to inspire biologists to seek evidence of these concepts in living organisms. This interplay of observations and theories is helping us understand how patterns like those on cheetahs develop.
This video was supported by Audible, which offers a vast selection of audiobooks, including “The Information” by science writer James Gleick. This book explores how figures like Alan Turing have contributed to our understanding of information and its transmission. To download “The Information” or another book of your choice and support MinuteEarth, visit www.audible.com/minuteearth.
Additionally, we previously conducted a survey about personal experiences with asparagus and received many insightful responses. You can find the results linked in the description below.
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This version maintains the core ideas while removing any informal or potentially inappropriate content.
Math – The abstract science of number, quantity, and space, either as abstract concepts (pure mathematics), or as applied to other disciplines such as physics and engineering (applied mathematics). – In advanced math courses, students explore complex equations that model real-world phenomena.
Patterns – Regular and intelligible forms or sequences discernible in the natural world or in a set of data. – Recognizing patterns in data sets is crucial for developing mathematical models in biology.
Activator – A molecule that increases the activity of an enzyme or a protein, often by binding to a specific site on the enzyme. – In genetic regulation, an activator can enhance the transcription of specific genes.
Inhibitor – A substance that slows down or prevents a particular chemical reaction or other processes. – Enzyme inhibitors are often used in drug development to block specific biological pathways.
Population – A group of individuals of the same species inhabiting a specific geographic area and capable of interbreeding. – The study of population dynamics is essential for understanding the spread of diseases in biology.
Genetic – Relating to genes or heredity, often involving the study of the structure and function of genes at a molecular level. – Genetic algorithms are used in computational biology to simulate the process of natural selection.
Structures – Arrangements or organizations of parts to form an organ, system, or living organism, or the arrangement of and relations between the parts or elements of something complex. – The study of protein structures is vital for understanding their functions in biological systems.
Theory – A supposition or a system of ideas intended to explain something, based on general principles independent of the thing to be explained. – The theory of evolution provides a framework for understanding the diversity of life on Earth.
Biology – The scientific study of life and living organisms, including their structure, function, growth, evolution, distribution, and taxonomy. – In biology, researchers often use mathematical models to simulate ecological systems.
Nature – The phenomena of the physical world collectively, including plants, animals, the landscape, and other features and products of the earth, as opposed to humans or human creations. – Understanding the mathematical principles underlying nature can lead to insights in both biology and physics.
