Show description

This is an example of a strange attractor; the Henon attractor, named after its discoverer, Michel Henon. Although composed of lines, orbits on this beast do not flow continuously, but hop from one location to another. When drawn, the Henon attractor seems to materialize out of nothing. It is also chaotic. All seed values that converge to the attractor do so in a different manner. 1 Strange Attractors separately. The Henon attractor also shows a great deal of fine structure (an infinite amount to be exact).

1 General Dimension A space is a collection of entities called points. Both terms are undefined but their relation is important: space is superordinate while point is subordinate. Our everyday notion of a point is that it is a position or location in a space that contains all the possible locations. Since everything doesn't happen in exactly the same place, we live in what can rightly be called a space, but points need not be point-like. Any kind of object can be a point. Other geometric objects, for instance, are totally acceptable (lines, planes, circles, ellipses, conic sections) as are algebraic entities (functions, variables, parameters, coefficients) or physical measurements (time, speed, temperature, index of refraction).

By embedding the set in the real number line, we could separate one point from any other with an irrational number. This set is has dimension 0, which would give the rational numbers a dimension of 1 (0 + 1 = 1). By embedding the set in the coordinate plane, we could also use any line with an x-intercept. This would give the rational numbers a dimension of 2 (1 + 1 = 2). We could also use planes if we embedded the set in a euclidean three-space and so on. I think it would be all right if we used the minimum value and called it the dimension of the space.