Fractals are the mathematical explanation of our world. Knowledge of fractals is essential to everyone's experience of their world. Here, I have explained the concept of fractals.
A discussion on the theory behind fractals, several different examples and applications of fractals in modern day life. This discusses the Coastline Paradox, Image Compression and uses within Creative Media
Fractals -A fractal is a natural phenomenon or a mathematical set .pdfLAMJM
Fractals -
A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that
displays at every scale. It is also known as expanding symmetry or evolving symmetry. If the
replication is exactly the same at every scale, it is called a self-similar pattern. An example of
this is the Menger Sponge.Fractals can also be nearly the same at different levels. This latter
pattern is illustrated in the small magnifications of the Mandelbrot set.Fractals also include the
idea of a detailed pattern that repeats itself.
Fractals are different from other geometric figures because of the way in which they scale.
Doubling the edge lengths of a polygon multiplies its area by four, which is two (the ratio of the
new to the old side length) raised to the power of two (the dimension of the space the polygon
resides in). Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is
two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere
resides in). But if a fractal\'s one-dimensional lengths are all doubled, the spatial content of the
fractal scales by a power that is not necessarily an integer. This power is called the fractal
dimension of the fractal, and it usually exceeds the fractal\'s topological dimension.
As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve
can be conceived of as winding through space differently from an ordinary line, still being a 1-
dimensional line yet having a fractal dimension indicating it also resembles a surface.
Fractal patterns have been modeled extensively, albeit within a range of scales rather than
infinitely, owing to the practical limits of physical time and space. Models may simulate
theoretical fractals or natural phenomena with fractal features. The outputs of the modeling
process may be highly artistic renderings, outputs for investigation, or benchmarks for fractal
analysis. Some specific applications of fractals to technology are listed elsewhere. Images and
other outputs of modeling are normally referred to as being \"fractals\" even if they do not have
strictly fractal characteristics, such as when it is possible to zoom into a region of the fractal
image that does not exhibit any fractal properties. Also, these may include calculation or display
artifacts which are not characteristics of true fractals.
Modeled fractals may be sounds,digital images, electrochemical patterns, circadian rhythms,etc.
Fractal patterns have been reconstructed in physical 3-dimensional spaceand virtually, often
called \"in silico\" modeling.Models of fractals are generally created using fractal-generating
software that implements techniques such as those outlined above.As one illustration, trees,
ferns, cells of the nervous system,blood and lung vasculature, and other branching patterns in
nature can be modeled on a computer by using recursive algorithms and L-systems
techniques.The recursive nature o.
Fractals are the mathematical explanation of our world. Knowledge of fractals is essential to everyone's experience of their world. Here, I have explained the concept of fractals.
A discussion on the theory behind fractals, several different examples and applications of fractals in modern day life. This discusses the Coastline Paradox, Image Compression and uses within Creative Media
Fractals -A fractal is a natural phenomenon or a mathematical set .pdfLAMJM
Fractals -
A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that
displays at every scale. It is also known as expanding symmetry or evolving symmetry. If the
replication is exactly the same at every scale, it is called a self-similar pattern. An example of
this is the Menger Sponge.Fractals can also be nearly the same at different levels. This latter
pattern is illustrated in the small magnifications of the Mandelbrot set.Fractals also include the
idea of a detailed pattern that repeats itself.
Fractals are different from other geometric figures because of the way in which they scale.
Doubling the edge lengths of a polygon multiplies its area by four, which is two (the ratio of the
new to the old side length) raised to the power of two (the dimension of the space the polygon
resides in). Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is
two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere
resides in). But if a fractal\'s one-dimensional lengths are all doubled, the spatial content of the
fractal scales by a power that is not necessarily an integer. This power is called the fractal
dimension of the fractal, and it usually exceeds the fractal\'s topological dimension.
As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve
can be conceived of as winding through space differently from an ordinary line, still being a 1-
dimensional line yet having a fractal dimension indicating it also resembles a surface.
Fractal patterns have been modeled extensively, albeit within a range of scales rather than
infinitely, owing to the practical limits of physical time and space. Models may simulate
theoretical fractals or natural phenomena with fractal features. The outputs of the modeling
process may be highly artistic renderings, outputs for investigation, or benchmarks for fractal
analysis. Some specific applications of fractals to technology are listed elsewhere. Images and
other outputs of modeling are normally referred to as being \"fractals\" even if they do not have
strictly fractal characteristics, such as when it is possible to zoom into a region of the fractal
image that does not exhibit any fractal properties. Also, these may include calculation or display
artifacts which are not characteristics of true fractals.
Modeled fractals may be sounds,digital images, electrochemical patterns, circadian rhythms,etc.
Fractal patterns have been reconstructed in physical 3-dimensional spaceand virtually, often
called \"in silico\" modeling.Models of fractals are generally created using fractal-generating
software that implements techniques such as those outlined above.As one illustration, trees,
ferns, cells of the nervous system,blood and lung vasculature, and other branching patterns in
nature can be modeled on a computer by using recursive algorithms and L-systems
techniques.The recursive nature o.
I made this slide about fractals for one of my math course's presentation. I chose fractal as it has this beautiful pattern and different kinds of variation.
ps- There might be some mistake. Your corrections will be appreciated.
Order, Chaos and the End of ReductionismJohn47Wind
The author presents a case against reductionism based on the emergence of chaos and order from underlying non-linear processes. Since all theories are mathematical, and based on an underlying premise of linearity, the author contends that there is no hope that science will succeed in creating a theory of everything that is complete. The controversial subject of life and evolution are explored, exposing the fallacy of a reductionist explanation, and offering a theory of order emerging from chaos as being the creative process of the universe, leading all the way up to consciousness. The essay concludes with the possibility that the three-dimensional universe is a fractal boundary that separates order and chaos in a higher dimension. The author discusses the work of Claude Shannon, Benoit Mandelbrot, Stephen Hawking, Carl Sagan, Albert Einstein, Erwin Schrodinger, Erik Verlinde, John Wheeler, Richard Maurice Bucke, Pierre Teilhard de Chardin, and others. This is a companion piece to the essay "Is Science Solving the Reality Riddle?"
Quantum phenomena modeled by interactions between many classical worldsLex Pit
Michael J. W. Hall, Dirk-André Deckert, and Howard M. Wiseman
ABSTRACT
We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical “worlds,” and quantum effects arise solely from a universal interaction between these worlds, without reference to any wave function. Here, a “world” means an entire universe with well-defined properties, determined by the classical configuration of its particles and fields. In our approach, each world evolves deterministically, probabilities arise due to ignorance as to which world a given observer occupies, and we argue that in the limit of infinitely many worlds the wave function can be recovered (as a secondary object) from the motion of these worlds. We introduce a simple model of such a “many interacting worlds” approach and show that it can reproduce some generic quantum phenomena—such as Ehrenfest’s theorem, wave packet spreading, barrier tunneling, and zero-point energy—as a direct consequence of mutual repulsion between worlds. Finally, we perform numerical simulations using our approach. We demonstrate, first, that it can be used to calculate quantum ground states, and second, that it is capable of reproducing, at least qualitatively, the double-slit interference phenomenon.
DOI: http://dx.doi.org/10.1103/PhysRevX.4.041013
Talk given in London, 3 January 2017. The talk has three aims:
(i) To clarify the use of these concepts (‘emergence’ and ‘reduction’) in science, especially in physics.
(ii) Specifically: to argue that the contrast ‘emergence vs. reduction’ poses a false dichotomy, since these two concepts are independent.
(iii) To point out that the independence of the two concepts may open interesting avenues for the philosophy of mind. But I will not work this out in a theory of the mind.
LIT 2001 FINAL EXAMPlease respond with a complete, thoughtful an.docxSHIVA101531
LIT 2001 FINAL EXAM
Please respond with a complete, thoughtful answer. Be sure to provide detail by referring to specific examples. DO NOT USE OUTSIDE RESEARCH SOURCES.
PART ONE: Answer ONE of the following questions:
1. Describe Langston Hughes’ view of America by tracing at least three of his poems. Also, describe the controversy around the manner in which Hughes portrayed African Americans in his poems.
2. William Carlos Williams uses an “open” style and format and Robert Frost uses a more “constructed”? What are the characteristics of each style – i.e., rhyme, etc. Use examples from their poems.
PART TWO: POEM ANALYSIS
DO NOT USE OUTSIDE RESEARCH SOURCES.
Critically analyze this poem by discussing three major components of analysis: Please read all 7 stanzas of the poem.
1. What are some of the structural elements of the poem? Metaphor, rhyme, symbols, sounds, etc.
2. What does the poem mean? Explain the content of the poem.
3. What is the theme of the poem?
To An Athlete Dying Young by A.E.Housman
The time you won our town the race
We chaired you through the market place;
Man and boy stood cheering by,
And home we brought you shoulder-high.
Today, the road all runners come,
Shoulder-high we bring you home,
And set you at your threshold down,
Townsman of a stiller town.
Smart lad, to slip betimes away
From fields where glory does not stay,
And early though the laurel grows
It withers quicker than the rose.
Eyes the shady night has shut
Cannot see the record cut,
And silence sounds no worse than cheers
After earth has stopped the ears:
Now you will not swell the rout
Of lads that wore their honors out,
Runners whom renown outran
And the name died before the man.
So set, before its echoes fade,
The fleet foot on the sill of shade,
And hold to the low lintel up
The still-defended challenge cup.
And round that early-laureled head
Will flock to gaze the strengthless dead
And find unwithered on its curls
The garland briefer than a girl’s.
Hubble's Law and the Expansion Rate of the Universe
This lab is based on the University of Washington’s “Hubble’s Law and the Expansion of
the Universe” lab. The website where the images and spectra are located is maintained
by the University of Washington Astronomy Department.
Learning Objectives
Using analyses of images and spectra of selected galaxies, you will
1. measure angular sizes of galaxies and find their distances,
2. measure the redshifts of galaxy spectral lines and find the recessional velocities
of the galaxies,
3. create a Hubble Plot to determine a value for Hubble's constant,
4. estimate the age of the Universe from this constant and compare that to the age
of the Sun and the Milky Way,
5. and summarize how our view of the Universe has changed as the value of the
Hubble constant has improved.
Background and Theory
In the 1920's, Edwin P. Hubble discovered a relationship, now known as Hubble' ...
Talk given at Oxford Philosophy of Physics, LSE's Sigma Club, the Munich Center for Mathematical Philosophy, Carlo Rovelli's 60th birthday conference.
I construe dualities in physics as particular cases of theoretical equivalence. The question then naturally arises whether duality is compatible with emergence. For the the focus of emergence is on novelty rather than on equivalence.
In the first part of the talk, I review recent work dealing with this question. I exhibit two ways in which duality and equivalence can be made compatible, and I give an example of emergence in gauge/gravity dualities: dualities between a theory of gravity in (d+1) dimensions and a quantum field theory (QFT) in d dimensions.
In the second part of the talk, I present new results on the question whether diffeomorphisms in gravity theories emerge from QFTs. I critically assess the following idea, taken from the physics literature: given that (a) the QFT is not a diffeomorphism invariant theory, and that (b) there is a duality between the QFT and the gravity theory, are we entitled to (c) conclude that the diffeomorphisms of the gravity theory emerge from the QFT?
I argue that one must distinguish different kinds of diffeomorphisms: some diffeomorphisms are ‘invisible’ to the QFT: all of the QFT’s quantities are invariant under them, therefore the QFT does not ‘see’ them. But other diffeomorphisms are ‘visible’ to the QFT. The invisible diffeomorphisms prompt a ‘Bulk Argument’, in analogy with the Hole Argument. The analysis of emergence is different for these different kinds of diffeomorphisms, and I discuss the way in which we can speak of emergence of diffeomorphisms in gauge/gravity dualities.
Book Formatting: Quality Control Checks for DesignersConfidence Ago
This presentation was made to help designers who work in publishing houses or format books for printing ensure quality.
Quality control is vital to every industry. This is why every department in a company need create a method they use in ensuring quality. This, perhaps, will not only improve the quality of products and bring errors to the barest minimum, but take it to a near perfect finish.
It is beyond a moot point that a good book will somewhat be judged by its cover, but the content of the book remains king. No matter how beautiful the cover, if the quality of writing or presentation is off, that will be a reason for readers not to come back to the book or recommend it.
So, this presentation points designers to some important things that may be missed by an editor that they could eventually discover and call the attention of the editor.
EASY TUTORIAL OF HOW TO USE CAPCUT BY: FEBLESS HERNANEFebless Hernane
CapCut is an easy-to-use video editing app perfect for beginners. To start, download and open CapCut on your phone. Tap "New Project" and select the videos or photos you want to edit. You can trim clips by dragging the edges, add text by tapping "Text," and include music by selecting "Audio." Enhance your video with filters and effects from the "Effects" menu. When you're happy with your video, tap the export button to save and share it. CapCut makes video editing simple and fun for everyone!
Can AI do good? at 'offtheCanvas' India HCI preludeAlan Dix
Invited talk at 'offtheCanvas' IndiaHCI prelude, 29th June 2024.
https://www.alandix.com/academic/talks/offtheCanvas-IndiaHCI2024/
The world is being changed fundamentally by AI and we are constantly faced with newspaper headlines about its harmful effects. However, there is also the potential to both ameliorate theses harms and use the new abilities of AI to transform society for the good. Can you make the difference?