How come your veins,lightning and the branches of a tree,all resemble one another???...tom science?

Answer 1

It is simply a manifestation of the same general phenomenon...controlled transport of something, whether it happens to be nutrients, water or electrons

Answer 2

The simple pattern of repeating bifurcation. You can add drainage patterns (as viewed on airphotos or imagery), though in a reverse direction.

The fractal geometry explanation is typical Physics overkill. Reminds me of the goofball character played by Jeff Goldblum in 'Jurassic Park'.

Answer 3

part is coincidence. part is it's the easiest design so nature goes with it. nature's fundamentally lazy and doesn't wanna expend energy so all life (and all processes) are designed around this fact

Answer 4

Didn't God design all things wonderfully?!!!

Answer 5

It is due to fractal geometry. In the book "Fractals", by John Briggs, (which I did not read yet) it is explained in detail.

"Fractals are unique patterns left behind by the unpredictable movements -- the chaos -- of the world at work. The branching patterns of trees, the veins in a hand, water twisting out of a running tap -- all of these are fractals. Learn to recognize them and you will never again see things in quite the same way.

Fractals permeate our lives, appearing in places as tiny as the surface of a virus and as majestic as the Grand Canyon. From ancient tribal peoples to modern painters to the animators of Star Wars, artists have been captivated by fractals and have utilized them in their work. Computer buffs are wild about fractals as well, for they can be generated on ordinary home computers."

"1.1 Fractal and Euclidean Geometries
Western culture is obsessed with order, smoothness and symmetry, to the point that we often impose on nature patterns and models derived from classical Greek geometry. Historically this tendency can be traced to Plato, for whom the 'real' world consisted of smooth, Euclidean shapes created by a supreme being. By contrast, the world we inhabit was created by a lesser, demiurgical being, and is nothing more than a rough, asymmetrical copy of the 'real' world. According to Plato, the 'real' world can only be glimpsed occasionally through the mind. In this way, Plato was able to reconcile the inability of classical geometry (as later formulated by Euclid) to describe the world we inhabit. Peters (1994) has described fractal geometry as that of the Demiurge.

Despite the fact that Euclidean geometry is a gross simplification of the world, western society has tenaciously clung to this ordered view. Such a view divorces us from nature, since we tend to perceive deviations from symmetry as fundamentally wrong, as something to be corrected. This is learned very early, for example when children are taught to represent complex natural objects such as trees as simple Euclidean constructs (e.g. triangles, circles, rectangles). In later life, we expend considerable effort creating and maintaining symmetric patterns in our gardens (Victorian topiary being an extreme example). Our architecture also reflects these deeply ingrained traditions of symmetry and order: a good early example is the Roman Pantheon, which incorporates three basic shapes of Euclidean geometry (the circle, triangle, and rectangle). More modern examples include the palaces of the French kings, the fascist architecture of Germany and Italy, and indeed any modern city skyline. It is instructive to note that human-made objects invariably stand out against the natural, more 'fractal' world.

1.2 What is Fractal Geometry?
Mandelbrot (1975) introduced the term 'fractal' (from the latin fractus, meaning 'broken') to characterize spatial or temporal phenomena that are continuous but not differentiable. Unlike more familiar Euclidean constructs, every attempt to split a fractal into smaller pieces results in the resolution of more structure. Fractal objects and processes are therefore said to display 'self-invariant' (self-similar or self-affine) properties (Hastings and Sugihara 1993). Self-similar objects are isotropic upon rescaling, whereas rescaling of self-affine objects is direction-dependent (anisotropic). Thus the trace of particulate Brownian motion in two-dimensional space is self-similar, whereas a plot of the x-coordinate of the particle as a function of time is self-affine (Brown 1995).

Fractal properties include scale independence, self-similarity, complexity, and infinite length or detail. Fractal structures do not have a single length scale, while fractal processes (time series) cannot be characterized by a single time scale (West and Goldberger 1987). Nonetheless, the necessary and sufficient conditions for an object (or process) to possess fractal properties have not been formally defined. Indeed, fractal geometry has been described as "a collection of examples, linked by a common point of view, not an organized theory" (Lorimer et al. 1994).

Fractal theory offers methods for describing the inherent irregularity of natural objects. In fractal analysis, the Euclidean concept of 'length' is viewed as a process. This process is characterized by a constant parameter D known as the fractal (or fractional) dimension. The fractal dimension can be viewed as a relative measure of complexity, or as an index of the scale-dependency of a pattern. Excellent summaries of basic concepts of fractal geometry can be found in Mandelbrot (1982), Frontier (1987), Schroeder (1991), Turcotte (1992), Hastings and Sugihara (1993), Lam and De Cola (1993) and in many of the references cited below.

The fractal dimension is a summary statistic measuring overall 'complexity'. Like many summary statistics (e.g. mean), it is obtained by 'averaging' variation in data structure (Normant and Tricot 1993). In doing so, information is necessarily lost. The estimated fractal dimension of a lakeshore, for example, tells us nothing about the actual size or overall shape of the lake, nor can we reproduce a map of the lake from D alone. However, the fractal dimension does tell us a great deal about the relative complexity of the lakeshore, and as such is an important descriptor when used in conjunction with other measures.

1.3 Fractals in the Biological Sciences
Biologists have traditionally modelled nature using Euclidean representations of natural objects or series. Examples include the representation of heart rates as sine waves, conifer trees as cones, animal habitats as simple areas, and cell membranes as curves or simple surfaces. However, scientists have come to recognize that many natural constructs are better characterized using fractal geometry. Biological systems and processes are typically characterized by many levels of substructure, with the same general pattern being repeated in an ever-decreasing cascade. Relationships that depend on scale have profound implications in human physiology (West and Goldberger 1987), ecology (Loehle 1983; Wiens 1989), and many other sub-disciplines of biology. The importance of fractal scaling has been recognized at virtually every level of biological organization (Fig. 1; Section 5).

Fractal geometry may prove to be a unifying theme in biology (Kenkel and Walker 1993), since it permits generalization of the fundamental concepts of dimension and length measurement. Most biological processes and structures are decidedly non-Euclidean, displaying discontinuities, jaggedness, and fragmentation. Classical measurement and scaling methods such as Euclidean geometry, calculus and the Fourier transform assume continuity and smoothness. However, it is important to recognize that while Euclidean geometry is not realized in nature, neither is strict mathematical fractal geometry. Specifically, there is a lower limit to self-similarity in most biological systems, and nature adds an element of randomness to its fractal structures. Nonetheless, fractal geometry is far closer to nature than is Euclidean geometry (Deering and West 1992).

The relevance of fractal theory to biological problems is dependent on objectives. To the forester interested in estimating stand board-feet, a Euclidean representation of a tree trunk (as a cylinder or elongated cone) may be quite adequate. However, for an ecologist interested in modelling habitat availability on tree trunks (say, for small epiphytes or invertebrates), fractal geometry is more appropriate. Using a fractal approach, the complex surface of tree bark is readily quantified. A forester's diameter tape ignores the surface roughness of the bark, giving but a crude estimate of the circumference of the trunk. For an insect 10 mm in length, the 'distance' that it must travel to circumnavigate the trunk is much greater than the measured diameter value. For an insect of length 1 mm, the distance travelled is greater still. This has consequences on the way that the tree trunk is perceived by organisms of different sizes. If the bark has a fractal dimension of D = 1.4, an insect an order of magnitude smaller than another perceives a length increase of 10D-1 = 100.4 = 2.51, or a habitat surface area increase of 2.512 = 6.31. By contrast, for a smooth Euclidean surface, D = 1 and both insects perceive the same 'amount' of habitat. The higher the fractal dimension D, the greater the perceived rate of increase in length (or surface) with decreasing scale."