Variables: End of Unit
Brownian Motion
Brownian motion is the observable phenomenon of the random motion of particles in a fluid (gas or liquid) resulting from their collision with the much smaller, much faster molecules of the fluid.
From Wikipedia
The Roman Lucretius’s scientific poem “On the Nature of Things” (c. 60 BC) has a remarkable description of Brownian motion of dust particles in verses 113–140 from Book II. He uses this as a proof of the existence of atoms:
“Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways… their dancing is an actual indication of underlying movements of matter that are hidden from our sight… It originates with the atoms which move of themselves [i.e., spontaneously]. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible.”
Although the mingling motion of dust particles is caused largely by air currents, the glittering, tumbling motion of small dust particles is, indeed, caused chiefly by true Brownian dynamics.
While Jan Ingenhousz described the irregular motion of coal dust particles on the surface of alcohol in 1785, the discovery of this phenomenon is often credited to the botanist Robert Brown in 1827. Brown was studying pollen grains of the plant Clarkia pulchella suspended in water under a microscope when he observed minute particles, ejected by the pollen grains, executing a jittery motion. By repeating the experiment with particles of inorganic matter he was able to rule out that the motion was life-related, although its origin was yet to be explained.
The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in a paper on the method of least squares published in 1880. This was followed independently by Louis Bachelier in 1900 in his PhD thesis “The theory of speculation”, in which he presented a stochastic analysis of the stock and option markets. The Brownian motion model of the stock market is often cited, but Benoit Mandelbrot rejected its applicability to stock price movements in part because these are discontinuous.[4]
Albert Einstein (in one of his 1905 papers) and Marian Smoluchowski (1906) brought the solution of the problem to the attention of physicists, and presented it as a way to indirectly confirm the existence of atoms and molecules. Their equations describing Brownian motion were subsequently verified by the experimental work of Jean Baptiste Perrin in 1908.
Assignment
Brownian Motion Art
Scientist, mathematicians, and artists have all been fascinated by Brownian motion. Using what we’ve learned so far create a digital wallpaper that is based on Brownian motion. Think of starting with one particle placed somewhere on the screen. Each time through draw() it will move, randomly. It may also change shape, color, size, or any other attribute. Does it always move the same distance every time? Without redrawing the background each frame, let the particle wander. The path it draws is what we are interested in. In order to receive full credit, you must use, JavaScript Objects, map(), random() and randomGaussian() in your sketch.
You may find these wallpapers inspiring.
https://www.deviantart.com/kaddar/art/Brownian-Motion-Mk-1-201790823
https://fublag.wordpress.com/tag/brownian-motion/
https://www.are.na/nic-schumann/random-noise
submit your code to Google Classroom
Read and Respond.
In addition to your sketch, consider the following quote
“We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.” — Pierre Simon Laplace, A Philosophical Essay on Probabilities
What Laplace is talking about here is what’s know as scientific determinism—the idea that if we were able to know exactly the current state of the universe, we could predict the future, i.e. nothing is truly random. What we perceive to be random is due to our incomplete understanding of the universe.
In about 250 words (~1 page), respond to the quote above. Do you agree or disagree with Laplace? What evidence do you have to support your position. Are there any assumptions that Laplace makes that are unfounded or unsupported?
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