gradient(redirected from Gradient of a scalar)
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in biology, a regular quantitative change in morphological or functional (including biochemical) properties along one of the axes of the body (or organ) at any stage of its development.
Examples of gradient include the diminution of yolk content in the eggs of amphibians in a direction from the vegetal pole to the animal pole and the varying sensitivity to poisons and dyes of different sections of the bodies of coelenterates and worms. A gradient that reflects decrease or increase in the rate of metabolism or other physiological indexes is called a physiological or metabolic gradient. An example in vertebrates of physiological gradient is the decrease in the capacity for automatic contraction in areas of the heart from the venous end to the aortal. The location of the highest manifestation of function is called the highest level of the gradient; the section with the lowest manifestation of function is called the lowest level of the gradient. According to the American scientist C. Child, physiological gradient is the primary cause of differentiation in the embryo and of integration in the adult organism; however, gradient frequently is not the cause but only the consequence of broader biological principles of development.
L. V. BELOUSOV
a vector indicating the direction of maximum change of some quantity, the value of which varies from point to point in space. If the quantity is expressed as the function u(x, y, z), then the components of the gradient are ∂u/∂x, ∂u/∂y, ∂u/∂z; gradient is denoted by the symbol grad u. At any point the gradient is normal to the constant-value surface of the function u(x, y, z) at that point and its magnitude is
The concept of gradient is widely used in physics, meteorology, oceanography, and other sciences to indicate the space rate of change of some quantity when shifting for the unit length in the direction of the gradient; for example, pressure gradient, temperature gradient, humidity gradient, gradient of wind velocity, gradient of salinity, gradient of ocean water density, and gradient of electrical potential, better known as electric field intensity.
gradientA smooth blending of shades from light to dark or from one color to another. In 2D drawing programs and paint programs, gradients are used to create colorful backgrounds and special effects as well as to simulate lights and shadows. In 3D graphics programs, lighting can be rendered automatically by the software. See 3D graphics.
|The software generates the gradient automatically as in this example created in Photoshop.|