prp ppt mavericks about mobius strip.pptx

about mobius strip an mathematical phenomenon

1. Chaos Theory

2. AGENDA Introduction History Fundamental concepts Lorenz attractors Examples Applications Related Advanced topics Conclusion

3. What is chaos theory? the branch of mathematics that deals with complex systems whose behavior is highly sensitive to slight changes in conditions, so that small alterations can give rise to strikingly great consequences.

4. HISTORY An American mathematician and meteorologist, Edward Lorenz's work in the 1960s played a pivotal role in the development of chaos theory he discovered that small differences in initial conditions could lead to vastly different outcomes. Lorenz's work highlighted the idea of deterministic chaos, where systems appear random but are governed by deterministic laws. This sensitivity to initial conditions was encapsulated in what is now famously known as the "butterfly effect," where a butterfly flapping its wings in Brazil could set off a chain of events leading to a tornado in Texas

5. F undamentals Of Chaos Theory 01 Nonlinear Dynamics 02 Bifurcations 03 Strange Attractors Chaos theory deals extensively with nonlinear dynamical systems, where the output is not directly proportional to the input. Nonlinear systems can exhibit complex behavior, including chaotic behavior, bifurcations, and attractors. Linear systems, by contrast, have outputs that are directly proportional to inputs and are generally more predictable. Bifurcations occur in nonlinear systems when a small change in a parameter causes a qualitative change in the system's behavior. They often lead to the creation or disappearance of periodic orbits, and they can give rise to chaotic behavior. Bifurcation diagrams are used to visualize how the system's behavior changes with varying parameters. A strange attractor is a type of attractor observed in chaotic systems. It is characterized by its fractal structure, meaning that it exhibits self-similarity at different scales. Strange attractors are "strange" because the system's behavior appears random yet is deterministic.

6. F undamentals Of Chaos Theory 04 05 06 Fractals Universality Deterministic Chaos Fractals are mathematical objects that exhibit self-similarity at different scales. Many chaotic systems produce fractal patterns when plotted, providing a way to visually represent their complexity. Fractals are used to describe irregular shapes found in nature and chaotic systems, such as coastlines, clouds, and the Mandelbrot set. In certain types of chaotic systems, a period-doubling route to chaos can be observed. This means that as a control parameter is increased, the system transitions from stable behavior to periodic behavior with a doubling period, eventually leading to chaos. The values at which these transitions occur exhibit universal constants known as the Feigenbaum constants, showing a remarkable consistency across different systems. Chaos theory challenges the traditional view of randomness by demonstrating that deterministic systems can exhibit behavior that appears random. This means that even though the system's behavior is governed by deterministic laws, it can be highly unpredictable due to sensitivity to initial conditions.

7. Lorentz attracters The Lorenz system consists of three nonlinear ordinary differential equations. [ Here, represents the rate of convection in the system] [ y represents the temperature variation of the rising air, and ρ is a parameter related to the Prandtl number and represents the Rayleigh number in fluid dynamics.] [ represents the vertical temperature gradient] The parameters σ , ρ , and β are positive constants. In the standard form, they are typically set to σ =10, ρ =28, and β =38​. These equations describe the evolution of the three variables x , y , and z over time. They capture the chaotic behavior of the system, particularly in modeling atmospheric convection.  

8. Whoa! This can be the part of the presentation where you introduce yourself, write your email…

9. Fractals and non-euclidean geometry Venus has a beautiful name and is the second planet from the Sun. It’s hot and has a poisonous atmosphere Mercury is the closest planet to the Sun and the smallest one in the Solar System it’s only a bit larger than the Moon Mercury Venus

10. The emergence of complexity Mercury is the closest planet to the Sun and the smallest of them all Venus has a beautiful name and is the second planet from the Sun Despite being red, Mars is actually a cold place. It’s full of iron oxide dust Mercury Venus Mars

11. Sensitivity to initial conditions Mars is actually a very cold place Venus has extremely high temperatures Jupiter is the biggest planet of them all Saturn is a gas giant and has several rings Mars Jupiter Venus Saturn

12. Neural networks and chaos Mars is actually a very cold place Venus has extremely high temperatures Neptune is the farthest planet from the Sun Saturn is a gas giant with several rings Mars Neptune Venus Saturn Jupiter is the biggest planet of them all Jupiter

13. Mercury is the closest planet to the Sun Saturn How complex systems learn Mars is actually a very cold place Neptune is the farthest planet from the Sun Saturn is a gas giant with several rings Venus Mars Venus has extremely high temperatures Neptune Mercury Jupiter is the biggest planet of them all Jupiter

14. Awesome words

15. “This is a quote, words full of wisdom that someone important said and that can inspire anyone who reads them” —Someone Famous

16. Chaos dynamics You can enter a subtitle here if you need it 02

17. A picture is worth a thousand words

18. The geometric shape of chaos dynamics Images reveal large amounts of data, so remember: use an image instead of a long text. Your audience will appreciate it

19. 98,300,000 Big numbers catch your audience’s attention

20. Jupiter's rotation period 9h 55m 23s 333,000 The Sun’s mass compared to Earth’s 386,000 km Distance between Earth and the Moon

21. Determinism Despite being red, Mars is actually a cold place How is chaos measured? 50 % 29 % 20 % Mercury is the closest planet to the Sun and the smallest of them Venus has a beautiful name and is the second planet from the Sun Sensitivity to initial conditions Strange attractors

22. Computer mockup You can replace the image on the screen with your own work. Just right-click on it and select “Replace image”

23. Tablet mockup You can replace the image on the screen with your own work. Just right-click on it and select “Replace image”

24. Phone mockup You can replace the image on the screen with your own work. Just right-click on it and select “Replace image”

25. Chaos in social networks Mars is actually a very cold place Venus has extremely high temperatures Jupiter is the biggest planet of them all Saturn is a gas giant and has several rings Mars Jupiter Venus Saturn

26. Complex systems 03 You can enter a subtitle here if you need it

27. Measuring chaos in complex systems Team A Team B Team C Team D Mercury 0.06 0.53 0.38 0.38 Mars 0.11 9.4 0.53 0.78 Saturn 95.2 1.16 9.4 1.16 Jupiter 104 1.23 10.3 1.23

28. The role of chaos in modern physics Venus is the second planet from the Sun Mercury is the closest planet to the Sun Mars is actually a very cold place Jupiter is the biggest planet of them all V IV I II III Saturn is a gas giant with several rings

29. Chaos and complexity in social networks & online communities Follow the link in the graph to modify its data and then paste the new one here. For more info, click here Venus has a beautiful name and is the second planet from the Sun Despite being red, Mars is actually a cold place. It’s full of iron oxide dust Venus Mars

30. The study of biological systems Mars is actually a very cold place Venus has extremely high temperatures Jupiter is the biggest planet of them all Saturn is a gas giant and has several rings Molecular Plants Zoology Neurobiology

31. Chaos simulation in computing Mercury Venus Mars Mercury is the closest planet to the Sun and the smallest of them all Venus has a beautiful name and is the second planet from the Sun Despite being red, Mars is actually a cold place. It’s full of iron oxide dust Sun Earth Venus Jupiter Mercury Moon Saturn Mars Ceres Neptune Uranus Pluto

32. Randomness & uncertainty Follow the link in the graph to modify its data and then paste the new one here. For more info, click here Venus has a beautiful name and is the second planet from the Sun Despite being red, Mars is actually a cold place. It’s full of iron oxide dust Venus Mars 59 % 41%

33. Chaos theory in economic theory Venus is the second planet from the Sun Saturn is composed of hydrogen and helium Neptune is the farthest planet from the Sun Despite being red, Mars is a cold place

34. Deterministic chaos vs randomness Solar System Jupiter Neptune It's also the fourth-largest planet by diameter in the Solar System This planet is one of the farthest planet from the Sun It was named after the Roman god of the skies and lightning It's a gas giant and the biggest planet in the Solar System

35. Bill Johnson Amy Edwards Our team You can speak a bit about this person here You can speak a bit about this person here

36. Thanks! Do you have any questions? [email protected] [phone] yourwebsite.com Please keep this slide for attribution

37. Here’s an assortment of alternative resources whose style fits that of this template: Photos: Theorem written in white chalk on school board Background of seamless kaleidoscope magnetic metallic shaving Modern form of ferromagnetic liquid metal with copy space Wonder wheel movement lights with light bulb Blurred night lights I Blurred night lights II Ferromagnetic fluid phenomenon with pink background Kaleidoscopic green abstract magnetic metallic shaving background Transparent bubbles and rainbow background Colorful trails of neon lights Alternative resources

38. Did you like the resources on this template? Get them on our other websites: Photos: Colorful decoration for new year party Blurred night lights Dynamic light painting background Rainbow lights prism effect Female researcher in the biotechnology laboratory Medium shot smiley scientist Resources

39. Instructions for use If you have a free account, in order to use this template, you must credit Slidesgo by keeping the Thanks slide. Please refer to the next slide to read the instructions for premium users. As a Free user, you are allowed to: Modify this template. Use it for both personal and commercial projects. You are not allowed to: Sublicense, sell or rent any of Slidesgo Content (or a modified version of Slidesgo Content). Distribute Slidesgo Content unless it has been expressly authorized by Slidesgo. Include Slidesgo Content in an online or offline database or file. Offer Slidesgo templates (or modified versions of Slidesgo templates) for download. Acquire the copyright of Slidesgo Content. For more information about editing slides, please read our FAQs or visit our blog: https://slidesgo.com/faqs and https://slidesgo.com/slidesgo-school

40. As a Premium user, you can use this template without attributing Slidesgo or keeping the Thanks slide. You are allowed to: Modify this template. Use it for both personal and commercial purposes. Hide or delete the “Thanks” slide and the mention to Slidesgo in the credits. Share this template in an editable format with people who are not part of your team. You are not allowed to: Sublicense, sell or rent this Slidesgo Template (or a modified version of this Slidesgo Template). Distribute this Slidesgo Template (or a modified version of this Slidesgo Template) or include it in a database or in any other product or service that offers downloadable images, icons or presentations that may be subject to distribution or resale. Use any of the elements that are part of this Slidesgo Template in an isolated and separated way from this Template. Register any of the elements that are part of this template as a trademark or logo, or register it as a work in an intellectual property registry or similar. For more information about editing slides, please read our FAQs or visit our blog: https://slidesgo.com/faqs and https://slidesgo.com/slidesgo-school Instructions for use (premium users)

41. This presentation has been made using the following fonts: Marcellus ( https://fonts.google.com/specimen/Marcellus ) Arsenal ( https://fonts.google.com/specimen/Arsenal ) #262628 #595959 Fonts & colors used #c2c2c2 #f2f2f2 #ffffff #9e9e9e

42. Create your Story with our illustrated concepts. Choose the style you like the most, edit its colors, pick the background and layers you want to show and bring them to life with the animator panel! It will boost your presentation. Check out h ow it works . Storyset Pana Amico Bro Rafiki Cuate

43. You can easily resize these resources without losing quality. To change the color , just ungroup the resource and click on the object you want to change. Then, click on the paint bucket and select the color you want. Group the resource again when you’re done. You can also look for more infographics on Slidesgo. Use our editable graphic resources...

44. JANUARY FEBRUARY MARCH APRIL PHASE 1 Task 1 Task 2 JANUARY FEBRUARY MARCH APRIL MAY JUNE PHASE 1 PHASE 2 Task 1 Task 2 Task 1 Task 2

45. You can resize these icons without losing quality. You can change the stroke and fill color ; just select the icon and click on the paint bucket/pen . In Google Slides, you can also use Flaticon’s extension , allowing you to customize and add even more icons. ...and our sets of editable icons

46. Educational Icons Medical Icons

47. Business Icons Teamwork Icons

48. Help & Support Icons Avatar Icons

49. Creative Process Icons Performing Arts Icons

50. Nature Icons

51. SEO & Marketing Icons