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In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines , are statistically self-similar: parts of them show the same statistical properties at many scales. [ 2 ]
We see that for ordinary self-similar objects, being n-dimensional means that when it is rep-tiled into pieces each scaled down by a scale-factor of 1/r, there are a total of r n pieces. Now, consider the Koch curve. It can be rep-tiled into four sub-copies, each scaled down by a scale-factor of 1/3.
The object began being thought of not as a fixed external object but also as an extension of our subjective self. One of the types of objects theorized in surrealism was the phantom object. According to Salvador Dalí , these objects have a minimum of mechanical meaning, but, when viewed, the mind evokes phantom images which are the result of ...
Self-similar processes are stochastic processes satisfying a mathematically precise version of the self-similarity property. Several related properties have this name, and some are defined here. A self-similar phenomenon behaves the same when viewed at different degrees of magnification, or different scales on a dimension.
The Taima mandala is based on the Contemplation Sutra, but other similar mandalas have been made subsequently. Unlike mandalas used in Vajrayana Buddhism, it is not used as an object of meditation or for esoteric ritual. Instead, it provides a visual representation of the Pure Land texts, and is used as a teaching aid.
The rule of similarity states that images that are similar to each other can be grouped together as being the same type of object or part of the same object. Therefore, the more similar two images or objects are, the more likely it will be that they can be grouped together. For example, two squares among many circles will be grouped together.
The self-similar solution of the second kind also appears in different contexts such as in boundary-layer problems subjected to small perturbations, [8] as was identified by Keith Stewartson, [9] Paul A. Libby and Herbert Fox. [10] Moffatt eddies are also a self-similar solution of the second kind.
Training in the visual arts has generally been through variations of the apprentice and workshop systems. In Europe, the Renaissance movement to increase the prestige of the artist led to the academy system for training artists, and today most of the people who are pursuing a career in the arts train in art schools at tertiary levels.