variation of the algorithm of the so called mandelbulb-object(done by n-th power of hypercomplex or triplex numbers). Squaring of hypercomplex numbers is done by going around the equator of the unit sphere(when the height is the z-value, the northern pole will lie on 1 on the z-axis), til the meridian will go through the point z. Then the angle between the equator and the line from zero to z and the equator will be doubled.(A program, performing this is integrated in Terry Gintz programs quasz and podme(hi Terry!) with the name "rings of fire"(because points on rings parallel to the equator will be projected to another such ring, the rings just moving, like rings of kodiac-light(?-Polarlichter) on a photo of a moon of jupiter, with such luminescent rings around the poles. Just had a near miss, tried n-fold angles, but missed to take the n-th power of the vector, but for n=2 the results are identical. Now, this structure here we get with the n-th power(instead of squaring) of an algorithm, which is called "ventri" in the fractal programs of Terry Gintz. "ventri" because the Julia sets resemble to brains with ventricles, this is not only just happening, it has a deeper meaning-see some papers"fractal neural nets" or "tomogaphy in factal neural nets", did some posters about this very,very exciting and promising field,(til now only very few took notice-pity),these nets, based on processing of memory-strings specific for each dynamic pattern in those Julia-set-nets are by far superior to those synaptic weight changing nets-we will see. Back to the artichoke and ventri: North pole lying at 1 on the x-axis, the equator of the unit sphere in y-z-plane(i use a coord-system oriented different to the most often used ones). We take the meridian through z, the angle of the meridian to the pos. y-axis being gamma(it´s the geographic length of z), the angle between the pos. x-axis(or the north pole) and the vector from zero to z will be measured, called alpha. Doubling only alpha, squaring the modulus of z will give the squaring of quaternions (with w=0). (z will move on its original meridian away from north pole, when doing higher powers of z in case of quaternions. The results, as we know, a little bit disappointing). Now in "ventri", the angle gamma will also be doubled(or taken to a higher power as well by multiplying with the value of"power"), while the point is moving its way on the meridian, the meridian is rotating around the x-axis simultaneously to the movement of the point. Without this additional movement, the points wander along perfect logarithmic spirals(as they do in the original Julia- and Mandelbrot-algo in 2D), in "ventri", the trajectories are sorts of logarithmic spirals, rotating not only around the center, but also around the x-axis.(The connection between math and biology is the logarithmc spiral, cells, wandering around in fields of growth-factors, are able to go along such trajectories, therefore it is not just happening by chance, such stuctures having biological appeal.(Doing it the reversed way, not squaring a number and so on, but starting with a sphere(starting with a bubble, we get ventruculi) of cells around zero, each cell dividing into two or more cells, these children-cells wandering to the roots of the starting place, bio-structure, brains can form such structures, if each neuronal cell will keep connection by its axon to its parent cell, we get a perfect threedimensional neural network, looking biological with gyri and lobes, fibres crossing somatotopic the midline(by squaring the points in some quadrants) and the full richness of intrastructural connectivity, enabling very interesting and elegant pattern detection and processing.-the starting with a bubble or sphere is just the well known orbit trap colouring, but not just to colour certain voxels, but to decide, whether they belong to the set(only voxels fulfilling being drawn). As far as i got, there is another important basic variation: Like in the mandelbulb-algo, but going along the loxodromic spiral through the point, which we get, where the line from zero through z will cross the unit sphere, when n-fold multiplying the angle theta in the mandelbulb algo. Then taking the n-power of the length of the original vector z and so on.(It is integrated as "loxodromic" in T.Gintz´s programs. With some variation, we get quite striking pictures). The video was made with chaospro by Martin Pfingstl-great program-iterations 27, 8th power
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Mandelbulb flightby shfractal5,973 views
....what is this for a silly shit??!!!!
masterbeefxD 2 years ago
it is just a variation of the so called mandelbulb-object, a fractal, maybe You like it or maybe not, in mathematical sense it is of some interest as a threedimensional extension of the famous and beautiful Mandelbrot set, its beauty is unreached til today by the threedimensional sets-we are just looking for the best looking 3D-structure, some sort of competition It is interesting how the fine structures(not really visible here) evolve, think it is not yet fully understood-just pictures
TRAJEKTORULM 2 years ago
@TRAJEKTORULM know whayne??
masterbeefxD 2 years ago
sorry, do not understand
TRAJEKTORULM 2 years ago