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Imag8nary numbers ethereal


imag8nary numbers ethereal

Amethystium is a music project aiming to create and explore emotive imaginary worlds in sound. Primarily electronic-based, the compositions traverse. Photographer Peter Treiber creates an imaginary universe in 'Ethereal but they do have numbers, such as "Ethereal Luminescence ," in. One of the important results from complex variables is that the exponential of an imaginary number corresponds to a rotation in the complex plane. FIXED ODDS BETTING TERMINALS REVIEW OF OPTOMETRY

A process given for the creation of quintessence is distillation of alcohol seven times. As early as the s, Newton used the idea of aether to help match observations to strict mechanical rules of his physics. These aether theories are considered to be scientifically obsolete, as the development of special relativity showed that Maxwell's equations do not require the aether for the transmission of these forces. Einstein noted that his own model which replaced these theories could itself be thought of as an aether, as it implied that the empty space between objects had its own physical properties.

It has also been called a fifth fundamental force. Aether and light[ edit ] Main article: Luminiferous aether The motion of light was a long-standing investigation in physics for hundreds of years before the 20th century. The use of aether to describe this motion was popular during the 17th and 18th centuries, including a theory proposed by Johann II Bernoulli , who was recognized in with the prize of the French Academy.

In his theory, all space is permeated by aether containing "excessively small whirlpools". These whirlpools allow for aether to have a certain elasticity, transmitting vibrations from the corpuscular packets of light as they travel through. At the time, it was thought that in order for light to travel through a vacuum, there must have been a medium filling the void through which it could propagate, as sound through air or ripples in a pool.

Later, when it was proved that the nature of light wave is transverse instead of longitudinal, Huygens' theory was replaced by subsequent theories proposed by Maxwell , Einstein and de Broglie , which rejected the existence and necessity of aether to explain the various optical phenomena.

These theories were supported by the results of the Michelson—Morley experiment in which evidence for the motion of aether was conclusively absent. He based the whole description of planetary motions on a theoretical law of dynamic interactions. He renounced standing attempts at accounting for this particular form of interaction between distant bodies by introducing a mechanism of propagation through an intervening medium. In his aether model, Newton describes aether as a medium that "flows" continually downward toward the Earth's surface and is partially absorbed and partially diffused.

This "circulation" of aether is what he associated the force of gravity with to help explain the action of gravity in a non-mechanical fashion. His theory also explains that aether was dense within objects and rare without them. As particles of denser aether interacted with the rare aether they were attracted back to the dense aether much like cooling vapors of water are attracted back to each other to form water. This elastic interaction is what caused the pull of gravity to take place, according to this early theory, and allowed an explanation for action at a distance instead of action through direct contact.

Experimentation after experimentation, I realized that really complex structures would emerge if I gave species the ability to eat the substrate of other species. Species can eat the substrate of other species Agents of a same specie would cluster together while avoiding clusters of other species, resulting in interesting large-scale behaviors.

Interesting large scale behaviors I based Ethereal Microcosm on this system. However, I wanted to push it further because I was still not happy with the overall complexity. First of all, I wanted to bring more diversity to the species. In the system above, all the agents had the same properties they all reacted to their substrate in the same way. By giving different properties to each species, I felt some more interesting behaviors would emerge.

Species have different properties Species have different properties colorized Finally, some inter-species mutations were added to the system. The properties of a specie could mutate when meeting other species. This component would allow for more complex behaviors over time and would make it harder for the system to reach a perfectly stable state, allowing for ever-evolving patterns.

Mutations inter-species Generative Art is essentially made of 2 components: the algorithmic system its sensorial representation most often visual In essence, agent-based systems manipulate points over time. If rendering those points directly can already be enough to represent an algorithmic system, I find it lacks some visual quality.

This is what Ethereal Microcosm would look like if only points were rendered: Ethereal Microcosm rendered with points In my quest of pushing systems to generate life-like patterns, it felt right to explore a realistic imagery to highlight their nature. And so I began experimenting with different techniques. A lot of different techniques. The quest of realistic-looking imagery For each new system I studied, I wanted to push the visual quality a bit further.

This is the same system Clusters X which went through a few visual updates over time: Increase in visual quality for Clusters X sorted by chronological order The render style of Ethereal Microcosm is the result of many months of exploration of various techniques. A lot of tiny details were added here and there. The system itself needs to be designed carefully. I wanted it to exhibit 2 visual properties: large scale patterns, similar to micro-biological entities small scale areas with high details, suggesting the existence of even more complex smaller processes The idea was to provide 2 levels of visual appreciation of the patterns.

When looking at the whole picture, the brain should recognize micro-biological entities. And when taking the time to observe smaller details, the brain should feel that if we were to zoom on specific areas, we would surely observe even more complex behaviors.

When I started working on the piece, I focused on finding stable states to generate large scale patterns. Finding large-scale behaviors Then, I explored the parametric space in various way to find a right balance between local and global complexity.

By adding interactions, playing with contrast, combining colors in specific ways, I was finally able to bring local complexity in the patterns. Local complexity When looking at those areas where it seems like there is a lot of details, the brain feels that the system must be even more complex at a smaller scale.

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It means the square of any real number is always positive. Then what number results in a negative square? It is an imaginary number. In math, we come across the square root of negative numbers many times, especially in the case of solving quadratic equations using the quadratic formula. In such cases, the usage of imaginary numbers is mandatory. We can see that each of these numbers is a product of a non-zero real number and i.

For example, a complex number i represents the point 1, -3 on the Argand plane. Thus, the imaginary numbers always lie on the vertical axis of an Argand plane. Here are a few examples. If we want to represent points in a plane using numbers, i must be a non-real number, in the sense that it must not lie in the Real set. We interpret i in math as follows: "i is one unit in the direction perpendicular to the real axis". In the above figure, we can see that the point 0, 1 is nothing but "i".

As we said earlier, the various different parts of the puzzle that is Complex Numbers will fall into place as you delve deeper into this subject. At this point, just keep in mind that: i is a non-real number it lies outside the Real set.

Instead, he said, "complex numbers really do exist. The equations used to describe the behavior of tiny quantum particles are expressed with these complex numbers. This raised a question, Scandolo told Live Science: Are these numbers just mathematical tools, or do they represent something real about the quantum states these equations describe? To find out, the researchers used a mathematical framework to determine if imaginary numbers are a "resource. Quantum entanglement is a resource in quantum theory, because it allows actions such as quantum teleportation, or the transfer of information between locations.

If imaginary numbers are a resource, they'd enable physicists to do more than they could if imaginary numbers weren't present. The team's calculations suggested that imaginary numbers are indeed a resource. But the next step was to check that math in the real world.

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Imaginary Numbers - Basic Introduction imag8nary numbers ethereal

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