# kb

id: patterns-in-nature-20260505-0
file: data/en.wikipedia.org/wiki/Patterns_in_nature-0.md
category: reference
title: Patterns in nature
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Patterns_in_nature
date_saved: 2026-05-05T03:12:13.121366+00:00
instance: kb-cron
parent: patterns-in-nature-20260505-0
summary:
Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time. In the 19th century, the Belgian physicist Joseph Plateau examined soap films, leading him to formulate the concept of a minimal surface. The German biologist and artist Ernst Haeckel painted hundreds of marine organisms to emphasise their symmetry. Scottish biologist D'Arcy Thompson pioneered the study of growth patterns in both plants and animals, showing that simple equations could explain spiral growth. In the 20th century, the English mathematician Alan Turing predicted mechanisms of morphogenesis which give rise to patterns of spots and stripes. The Hungarian biologist Aristid Lindenmayer and the French American mathematician Benoît Mandelbrot showed how the mathematics of fractals could create plant growth patterns. Mathematics, physics and chemistry can explain patterns in nature at different levels and scales. Patterns in living things are explained by the biological processes of natural selection and sexual selection.


id: patterns-in-nature-20260505-1
file: data/en.wikipedia.org/wiki/Patterns_in_nature-1.md
category: reference
title: Patterns in nature
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Patterns_in_nature
date_saved: 2026-05-05T03:12:13.121366+00:00
instance: kb-cron
parent: patterns-in-nature-20260505-0
summary:
Living things like orchids, hummingbirds, and the peacock's tail have abstract designs with a beauty of form, pattern and colour that artists struggle to match. The beauty that people perceive in nature has causes at different levels, notably in the mathematics that governs what patterns can physically form, and among living things in the effects of natural selection, that govern how patterns evolve. Mathematics seeks to discover and explain abstract patterns or regularities of all kinds. Visual patterns in nature find explanations in chaos theory, fractals, logarithmic spirals, topology and other mathematical patterns. For example, L-systems form convincing models of different patterns of tree growth. The laws of physics apply the abstractions of mathematics to the real world, often as if it were perfect. For example, a crystal is perfect when it has no structural defects such as dislocations and is fully symmetric. Exact mathematical perfection can only approximate real objects. Visible patterns in nature are governed by physical laws; for example, meanders can be explained using fluid dynamics. In biology, natural selection can cause the development of patterns in living things for several reasons, including camouflage, sexual selection, and different kinds of signalling, including mimicry and cleaning symbiosis. In


id: patterns-in-nature-20260505-2
file: data/en.wikipedia.org/wiki/Patterns_in_nature-2.md
category: reference
title: Patterns in nature
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Patterns_in_nature
date_saved: 2026-05-05T03:12:13.121366+00:00
instance: kb-cron
parent: patterns-in-nature-20260505-0
summary:
Spirals are common in plants and in some animals, notably molluscs. For example, in the nautilus, a cephalopod mollusc, each chamber of its shell is an approximate copy of the next one, scaled by a constant factor and arranged in a logarithmic spiral. Given a modern understanding of fractals, a growth spiral can be seen as a special case of self-similarity. Plant spirals can be seen in phyllotaxis, the arrangement of leaves on a stem, and in the arrangement (parastichy) of other parts as in composite flower heads and seed heads like the sunflower or fruit structures like the pineapple and snake fruit, as well as in the pattern of scales in pine cones, where multiple spirals run both clockwise and anticlockwise. These arrangements have explanations at different levels – mathematics, physics, chemistry, biology – each individually correct, but all necessary together. Phyllotaxis spirals can be generated from Fibonacci ratios: the Fibonacci sequence runs 1, 1, 2, 3, 5, 8, 13... (each subsequent number being the sum of the two preceding ones). For example, when leaves alternate up a stem, one rotation of the spiral touches two leaves, so the pattern or ratio is 1/2. In hazel the ratio is


id: patterns-in-nature-20260505-3
file: data/en.wikipedia.org/wiki/Patterns_in_nature-3.md
category: reference
title: Patterns in nature
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Patterns_in_nature
date_saved: 2026-05-05T03:12:13.121366+00:00
instance: kb-cron
parent: patterns-in-nature-20260505-0
summary:
=== Bubbles, foam === A soap bubble forms a sphere, a surface with minimal area (minimal surface) — the smallest possible surface area for the volume enclosed. Two bubbles together form a more complex shape: the outer surfaces of both bubbles are spherical; these surfaces are joined by a third spherical surface as the smaller bubble bulges slightly into the larger one. A foam is a mass of bubbles; foams of different materials occur in nature. Foams composed of soap films obey Plateau's laws, which require three soap films to meet at each edge at 120° and four soap edges to meet at each vertex at the tetrahedral angle of about 109.5°. Plateau's laws further require films to be smooth and continuous, and to have a constant average curvature at every point. For example, a film may remain nearly flat on average by being curved up in one direction (say, left to right) while being curved downwards in another direction (say, front to back). Structures with minimal surfaces can be used as tents. At the scale of living cells, foam patterns are common; radiolarians, sponge spicules, silicoflagellate exoskeletons and the calcite skeleton of a sea urchin, Cidaris rugosa, all resemble


id: patterns-in-nature-20260505-4
file: data/en.wikipedia.org/wiki/Patterns_in_nature-4.md
category: reference
title: Patterns in nature
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Patterns_in_nature
date_saved: 2026-05-05T03:12:13.121366+00:00
instance: kb-cron
parent: patterns-in-nature-20260505-0
summary:
Alan Turing, and later the mathematical biologist James Murray, described a mechanism that spontaneously creates spotted or striped patterns: a reaction–diffusion system. The cells of a young organism have genes that can be switched on by a chemical signal, a morphogen, resulting in the growth of a certain type of structure, say a darkly pigmented patch of skin. If the morphogen is present everywhere, the result is an even pigmentation, as in a black leopard. But if it is unevenly distributed, spots or stripes can result. Turing suggested that there could be feedback control of the production of the morphogen itself. This could cause continuous fluctuations in the amount of morphogen as it diffused around the body. A second mechanism is needed to create standing wave patterns (to result in spots or stripes): an inhibitor chemical that switches off production of the morphogen, and that itself diffuses through the body more quickly than the morphogen, resulting in an activator-inhibitor scheme. The Belousov–Zhabotinsky reaction is a non-biological example of this kind of scheme, a chemical oscillator. Later research has managed to create convincing models of patterns as diverse as zebra stripes, giraffe blotches, jaguar spots (medium-dark patches surrounded by dark broken


id: physica-speculatio-20260505-0
file: data/en.wikipedia.org/wiki/Physica_speculatio-0.md
category: reference
title: Physica speculatio
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physica_speculatio
date_saved: 2026-05-05T03:12:14.303872+00:00
instance: kb-cron
parent: physica-speculatio-20260505-0
summary:
Physica speculatio is a text of scientific character written by Alonso de la Vera Cruz in 1557 in the capital of New Spain. It was the first published work in the American continent that specifically addressed the study of physics, and was written to teach the students of the Real University of Mexico. It introduced the main theoretical concepts of geocentric astronomy and references the heliocentric model. Fray Alonso de la Vera Cruz published in the capital of New Spain a Course of Arts, constituted in three volumes in Latin. The first form in 1553 under the title of Recognitio Summularum, that had like purpose help to the students of the Real University of Mexico to understand the philosophy by means of the understanding of the formal logic. A year afterwards appeared the second called Dialectica Resolutio, that was a continuation of the previous. The last was Physica speculatio. They did four editions, the last 3 of which were for use of the salmantino students and were abbreviated versions of the Mexican one. == Subjects == The Physica speculatio has by object the study or "investigation" -speculatio- and the exhibition, in general, of subjects of physics on the nature -Physica-,


id: physics-aristotle-20260505-0
file: data/en.wikipedia.org/wiki/Physics_(Aristotle)-0.md
category: reference
title: Physics (Aristotle)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physics_(Aristotle)
date_saved: 2026-05-05T03:12:15.422292+00:00
instance: kb-cron
parent: physics-aristotle-20260505-0
summary:
The Physics (Ancient Greek: Φυσικής ἀκρόασις, romanized: Physikḗs akróasis, or: Φυσικής ακροάσεως, Physikḗs akroáseōs; Latin: Physica or Naturales Auscultationes, possibly meaning "Lectures on nature") is a named text, written in ancient Greek, collated from a collection of surviving manuscripts known as the Corpus Aristotelicum, attributed to the 4th-century BC philosopher Aristotle. == The meaning of physics in Aristotle == It is a collection of treatises or lessons that deals with the most general (philosophical) principles of natural or moving things, both living and non-living, rather than physical theories (in the modern sense) or investigations of the particular contents of the universe. The chief purpose of the work is to discover the principles and causes of (and not merely to describe) change, or movement, or motion (κίνησις kinesis), especially that of natural wholes (mostly living things, but also inanimate wholes like the cosmos). In the conventional Andronicean ordering of Aristotle's works, it stands at the head of, as well as being foundational to, the long series of physical, cosmological and biological treatises, whose ancient Greek title, τὰ φυσικά, means "the [writings] on nature" or "natural philosophy". == Description of the content == The Physics is composed of eight books, which are


id: physics-aristotle-20260505-1
file: data/en.wikipedia.org/wiki/Physics_(Aristotle)-1.md
category: reference
title: Physics (Aristotle)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physics_(Aristotle)
date_saved: 2026-05-05T03:12:15.422292+00:00
instance: kb-cron
parent: physics-aristotle-20260505-0
summary:
The necessary in nature, then, is plainly what we call by the name of matter, and the changes in it. Both causes must be stated by the physicist, but especially the end; for that is the cause of the matter, not vice versa; and the end is 'that for the sake of which', and the beginning starts from the definition or essence… In chapter 3, Aristotle presents his theory of the four causes (material, efficient, formal, and final). Material cause explains what something is made of (for example, the wood of a house), formal cause explains the form which a thing follows to become that thing (the plans of an architect to build a house), efficient cause is the actual source of the change (the physical building of the house), and final cause is the intended purpose of the change (the final product of the house and its purpose as a shelter and home). Of particular importance is the final cause or purpose (telos). It is a common mistake to conceive of the four causes as additive or alternative forces pushing or pulling; in reality, all four are needed to explain (7.198a22-25). What we typically mean by cause in the


id: physics-aristotle-20260505-2
file: data/en.wikipedia.org/wiki/Physics_(Aristotle)-2.md
category: reference
title: Physics (Aristotle)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physics_(Aristotle)
date_saved: 2026-05-05T03:12:15.422292+00:00
instance: kb-cron
parent: physics-aristotle-20260505-0
summary:
=== Book VII (Η; 241a25–250b7) === Book VII briefly deals with the relationship of the moved to his mover, which Aristotle describes in substantial divergence with Plato's theory of the soul as capable of setting itself in motion (Laws book X, Phaedrus, Phaedo). Everything which moves is moved by another. He then tries to correlate the species of motion and their speeds, with the local change (locomotion, phorà) as the most fundamental to which the others can be reduced. Book VII.1-3 also exist in an alternative version, not included in the Bekker edition. === Book VIII (Θ; 250a14–267b26) === Book VIII (which occupies almost a fourth of the entire Physics, and probably constituted originally an independent course of lessons) discusses two main topics, though with a wide deployment of arguments: the time limits of the universe, and the existence of a Prime Mover — eternal, indivisible, without parts and without magnitude. Isn't the universe eternal, has it had a beginning, will it ever end? Aristotle's response, as a Greek, could hardly be affirmative, never having been told of a creatio ex nihilo, but he also has philosophical reasons for denying that motion had not always existed, on the grounds of


id: physics-aristotle-20260505-3
file: data/en.wikipedia.org/wiki/Physics_(Aristotle)-3.md
category: reference
title: Physics (Aristotle)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physics_(Aristotle)
date_saved: 2026-05-05T03:12:15.422292+00:00
instance: kb-cron
parent: physics-aristotle-20260505-0
summary:
=== Classical and medieval commentaries on the Physics === A commentary differs from a note in being a distinct work analyzing the language and subsumed concepts of some other work classically notable. A note appears within the annotated work on the same page or in a separate list. Commentaries are typically arranged by lemmas, or quotes from the notable work, followed by an analysis of the author of the commentary. The commentaries on every work of Aristotle are a vast and mainly unpublished topic. They extend continuously from the death of the philosopher, representing the entire history of Graeco-Roman philosophy. There are thousands of commentators and commentaries known wholly or more typically in fragments of manuscripts. The latter especially occupy the vaults of institutions formerly responsible for copying them, such as monasteries. The process of publishing them is slow and ongoing. Below is a brief representative bibliography of published commentaries on Aristotle's Physics available on or through the Internet. Like the topic itself, they are perforce multi-cultural, but English has been favored, as well as the original languages, ancient Greek and Latin. === Some modern commentaries, monographs and articles === == Further reading == Books Die Aristotelische Physik, W. Wieland,


