# Evolutionary Medicine

## CONTENTS OF CURRICULUM UNIT 09.05.09

## Math Morphing Proximate and Evolutionary Mechanisms

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## Glossary of Terms

Apollonian gasket: or Apollonian net is a fractal generated from triples of circles, where any circle is tangent to two others, named after Greek mathematician Apollonius of Perga.

Bacteriophages: any one of a number of viruses that infect bacteria, from "bacteria" and the Greek Φ?ΓΕΙΝ phagein "to eat."

Bifurcation theory: is the mathematical study of changes in the qualitative or topological structure of a given family. Examples of such families are the integral curves of a family of vector fields or, the solutions of a family of differential equations.

Butterfly effect: is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a dynamical system may produce large variations in the long term behavior of the system.

Chaos theory: a branch of mathematical and physical theory that deals with the nature and consequences of chaos and chaotic systems.

Complexity: a whole made up of complicated or interrelated parts.

Constructal theory: is the mental viewing that the generation of design, configuration, pattern, and geometry in nature is the physics phenomenon that unites all animate and inanimate systems, and that this phenomenon is covered by the Constructal Law stated by Adrian Bejan in 1996.

Contraction mapping theorem: or contraction mapping principle is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self maps of metric spaces, and provides a constructive method to find those fixed points. The theorem is named after Stefan Banach (1892-1945), and was first stated by him in 1922.

Diamond-square algorithm: is a method for generating highly realistic heightmaps for computer graphics. It is a slightly better algorithm than the three-dimensional implementation of the midpoint displacement algorithm which produces two-dimensional landscapes, and is also known as the random midpoint displacement fractal, the cloud fractal or the plasma fractal, because of the plasma effect produced when applied.

DNA knots: contains the genetic information that allows all modern living things to function, grow and reproduce however, it is unclear how long in the 4-billion-year history of life DNA has performed this function, as it has been proposed that the earliest forms of life may have used RNA as their genetic material.

Droste effect: The Droste effect is a Dutch term for a specific kind of recursive picture, one that in heraldry is termed mise en abyme. An image exhibiting the Droste effect depicts a smaller version of itself in a place where a similar picture would realistically be expected to appear. This smaller version then depicts an even smaller version of itself in the same place, and so on. Only in theory could this go on forever; practically, it continues only as long as the resolution of the picture allows, which is relatively short, since each iteration exponentially reduces the picture's size. It is a visual example of a strange loop, a self-referential system.

Evolution: is the change in the genetic material of a population of organisms from one generation to the next. Small differences can accumulate over time with each generation, which can manifest substantial changes in the organisms, and the emergence of new species.

Feigenbaum function: has been used to describe two different functions introduced by the physicist Mitchell Feigenbaum, in the study of dynamical systems.

Fractal art: is created by calculating fractal objects and representing the calculation results as still images, animations, music, or other media.

Fractal compression: applies algorithms convert geometric shapes into mathematical data called fractal codes which are used to recreate the encoded image. Fractal compression differs from pixel-based compression schemes such as JPEG, GIF and MPEG since no pixels are saved. Once an image has been converted into fractal code its relationship to any specific resolution is irrelevant, and it becomes resolution independent.

Fractal flames: are a member of the iterated function system class of fractals created by Scott Draves in 1992, and differ from ordinary iterated function systems in three ways: nonlinear functions are iterated instead of affine transforms; log-density display instead of linear or binary, a form of tone mapping; and color by structure or by the recursive path taken, instead of monochrome or by density.

Fractals: any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size

Fractal landscape: is a surface generated using a stochastic algorithm designed to produce fractal attributes that mimic the appearance of natural terrains; the result of which is not a deterministic fractal surface, but rather a random surface which displays fractal attributes

Fractal transform: is a technique invented by Michael Barnsley et al. to perform lossy image compression. This first practical fractal compression system for digital images resembles a vector system using the image itself as the codebook.

Fractint: is a freeware software package that can render and display many kinds of fractals. Its name comes from the words fractal and integer, since the first versions of it computed fractals by using only integer arithmetic (also known as fixed-point arithmetic), which led to much faster rendering on x86 computers without math coprocessors.

Fracton: is a collective quantized vibration on a substrate with a fractal structure, and are the fractal analog of phonons.

Geometric progressions: a sequence, such as 1,
^{
1
}
⁄
_{
2
}
,
^{
1
}
⁄
_{
4,
}
in which the ratio of a term to its predecessor is always the same, also called a geometrical progression or geometric sequence.

Graftal: or L-system is a formal grammar used in computer graphics to recursively define branching tree and plant shapes in a compact format.

Greeble: or nurnie is a small piece of detailing added to break up the surface of an object to add visual interest to a surface or object, particularly in movie special effects.

Iteration: a procedure in which repetition of a sequence of operations yields results successively closer to a desired result.

Lacunarity: is a measure of how a fractal fills space, and is used to further classify fractals and textures which, while sharing the same fractal dimension, appear very different visually. Dense fractals have a low lacunarity, and as the coarseness of the fractal increases, so does the lacunarity.

List of fractals by Hausdorff dimension: one of the essential features of a fractal is that its Hausdorff dimension strictly exceeds its topological dimension.

Mathematical knots: is an embedding of a circle in 3-dimensional Euclidean space.

Mitochondria: any of various round or long cellular organelles of most eukaryotes that are found outside the nucleus, produce energy for the cell through cellular respiration, and are rich in fats, proteins, and enzymes.

Newton fractal: is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial.

Recursion: the determination of a succession of elements, such as numbers or functions, by operation on one or more preceding elements according to algorithms, rules, or formulas, involving a finite number of steps or iterations.

Sacred geometry: Sacred geometry is geometry used in the design of sacred architecture and sacred art, with.the basic belief is that geometry and mathematical ratios, harmonics and proportion are also found in music, light, and cosmology.

Self-reference: referring to, or towards oneself or itself.

Sierpinski triangle: a fractal named after the Polish mathematician Wac?aw Sierpi¨½ski who described it in 1915, also called the Sierpinski gasket or the Sierpinski Sieve.

Space-filling curve: a continuous curve in 2, or 3, or higher dimensions can be thought of as the path of a continuously moving point, and to eliminate the inherent vagueness of this notion, brought to light by Peano's discovery, Jordan in 1887 introduced the following rigorous definition, which has since been adopted as the precise description of the notion of a continuous curve.

Strange loop: A strange loop is a hierarchy of levels, each of which is linked to at least one other by some type of relationship.

Tripanosomes: any of a genus (Trypanosoma) of parasitic flagellate protozoans that infest the blood of various vertebrates including humans, are usually transmitted by the bite of an insect, and include some that cause serious diseases, such as sleeping sickness and Chagas' disease.

Turbulence: irregular motion or agitation especially when characterized by up-and-down currents