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如贝纳尔细胞、激光、条状云或卷状云、冰柱上的涟漪、泥路上的洗衣板等图案以及凝固中的树枝状、液晶、孤子等。
如贝纳尔细胞、激光、条状云或卷状云、冰柱上的涟漪、泥路上的洗衣板等图案以及凝固中的树枝状、液晶、孤子等。
'''Rayleigh-Bénard convection''' is a type of natural convection, occurring in a planar horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as '''Bénard cells'''. Bénard–Rayleigh convection is one of the most commonly studied convection phenomena because of its analytical and experimental accessibility. The convection patterns are the most carefully examined example of self-organizing nonlinear systems.
Buoyancy, and hence gravity, are responsible for the appearance of convection cells. The initial movement is the upwelling of lesser density fluid from the heated bottom layer. This upwelling spontaneously organizes into a regular pattern of cells.
In mathematics and physics, a '''soliton''' or '''solitary wave''' is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. (Dispersive effects are a property of certain systems where the speed of a wave depends on its frequency.) Solitons are the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems.
The soliton phenomenon was first described in 1834 by John Scott Russell (1808–1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation".
===Mathematics===
===Mathematics===
Sphere packings and coverings. Mathematics underlies the other pattern formation mechanisms listed.
Sphere packings and coverings. Mathematics underlies the other pattern formation mechanisms listed.
球形填充和覆盖物。数学是其他斑图生成机制的基础。
In geometry, a '''sphere packing''' is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.
A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible. The proportion of space filled by the spheres is called the density of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume.
For equal spheres in three dimensions, the densest packing uses approximately 74% of the volume. A random packing of equal spheres generally has a density around 64%.
{{further|Gradient pattern analysis}}
{{further|Gradient pattern analysis}}