How many circles in an Apollonian gasket?
The table lists the curvatures of the largest circles in the gasket. Only the first three curvatures (of the five displayed in the table) are needed to completely describe each gasket – all other curvatures can be derived from these three. … Integral Apollonian gaskets.
| Beginning curvatures | Symmetry |
|---|---|
| −15, 32, 32, 33, 65 | D1 |
Who discovered the Apollonian gasket?
The mathematics tools used to solve the problem are known since René Descartes, and were re-discovered by Frederick Soddy, who published his solution in 1936 in the form of a poem in Nature [3]. Computing Apollonian gaskets is an interesting and not so difficult programming exercise.
When was the Apollonian Gasket discovered?
This fact was discovered in the late 1990s by Allan Wilks and Colin Mallows of AT&T Labs, and Wilks used it to write a very efficient computer program for plotting Apollonian gaskets.
What is the meaning Apollonian?
Apollonian, of, relating to, or resembling the god Apollo. Friedrich Nietzsche used the term in his book The Birth of Tragedy to describe one of the two opposing tendencies or elements in Greek tragedy. According to Nietzsche, the Apollonian attributes are reason, culture, harmony, and restraint.
What is the difference between Apollonian and Dionysian?
Apollo represents harmony, progress, clarity, logic and the principle of individuation, whereas Dionysus represents disorder, intoxication, emotion, ecstasy and unity (hence the omission of the principle of individuation).
How do you pack circles?
A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres is called a sphere packing. … Circle Packing.
| exact | approx. | |
|---|---|---|
| 5 | 2.70130… | |
| 6 | 3 | 3.00000 |
| 7 | 3 | 3.00000 |
| 8 | 3.30476… |
What is fractal nature?
A fractal is a kind of pattern that we observe often in nature and in art. As Ben Weiss explains, “whenever you observe a series of patterns repeating over and over again, at many different scales, and where any small part resembles the whole, that’s a fractal.”
Are fractals infinite?
A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos.
Is Sierpinski triangle a fractal?
The Sierpinski triangle is a self-similar fractal. It consists of an equilateral triangle, with smaller equilateral triangles recursively removed from its remaining area. … He also invented many popular fractals, including the Sierpinski triangle, the Sierpinski carpet and the Sierpinski curve.
What is a synonym for Apollonian?
consonant, eurythmic. (or eurhythmic), harmonic, harmonious.
What is an Arcadian person?
(Entry 1 of 2) 1 often not capitalized : a person who lives a simple quiet life. 2 : a native or inhabitant of Arcadia. 3 : the dialect of ancient Greek used in Arcadia.
How do you use Apollonian in a sentence?
Leonardo, the scientific rationalist and inventor, is an Apollonian (his work is owned by, among others, the archrationalist Bill Gates). Armani, with his serene, muted tones and clean lines, is the Apollonian designer.
What is Apollonian and Dionysian examples?
All types of form or structure are Apollonian, thus, sculpture is the most Apollonian of the arts, since it relies entirely on form for its effect. Rational thought is also Apollonian since it is structured and makes distinctions. Drunkenness and madness are Dionysian All forms of enthusiasm and ecstasy are Dionysian.
Why did Nietzsche Love Dionysus?
Dionysus is the Greek god of wine and music, and Nietzsche identifies the Dionysian as a frenzy of self-forgetting in which the self gives way to a primal unity where individuals are at one with others and with nature. Both the Apollonian and the Dionysian are necessary in the creation of art.
What is the popcorn syndrome?
The Popcorn Syndrome is the aftermath of having enjoyed a night at the movies (and eating popcorn), but waking up the next day and, in retrospect, realizing the many flaws in what was seen.
What is circular packing?
In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
What is efficiency in packing?
The packing efficiency is the fraction of the crystal (or unit cell) actually occupied by the atoms. It must always be less than 100% because it is impossible to pack spheres (atoms are usually spherical) without having some empty space between them.
What is cubic close packing?
Cubic Close Packing. Face Centered Cubic Cell. Closest packed means that the atoms are packed together as closely as possible. The FCC unit cell is actually made of four cubic close packed layers (click to show the unit cell with layers). The first layer of atoms pack together as close as possible.
What are fractals good for?
Fractals help us study and understand important scientific concepts, such as the way bacteria grow, patterns in freezing water (snowflakes) and brain waves, for example. … Wireless cell phone antennas use a fractal pattern to pick up the signals better, and pick up a wider range of signals, rather than a simple antenna.
Are humans fractals?
We are fractal. Our lungs, our circulatory system, our brains are like trees. They are fractal structures. … Most natural objects – and that includes us human beings – are composed of many different types of fractals woven into each other, each with parts which have different fractal dimensions.
What are examples of fractals?
Examples of fractals in nature are snowflakes, trees branching, lightning, and ferns.
Is Fibonacci a fractal?
The Fibonacci Spiral, which is my key aesthetic focus of this project, is a simple logarithmic spiral based upon Fibonacci numbers, and the golden ratio, Φ. Because this spiral is logarithmic, the curve appears the same at every scale, and can thus be considered fractal.
Is a circle a fractal?
The most iconic examples of fractals have bumps along their boundaries, and if you zoom in on any bump, it will be covered in bumps, etc etc. Both a circle and a line segment have Hausdorff dimension 1, so from this perspective it’s a very boring fractal.
Is a snowflake a fractal?
Part of the magic of snowflake crystals are that they are fractals, patterns formed from chaotic equations that contain self-similar patterns of complexity increasing with magnification. If you divide a fractal pattern into parts you get a nearly identical copy of the whole in a reduced size.
Graduated from ENSAT (national agronomic school of Toulouse) in plant sciences in 2018, I pursued a CIFRE doctorate under contract with Sun’Agri and INRAE in Avignon between 2019 and 2022. My thesis aimed to study dynamic agrivoltaic systems, in my case in arboriculture. I love to write and share science related Stuff Here on my Website. I am currently continuing at Sun’Agri as an R&D engineer.