Fractal Pendulum

(Be sure to set the video at HD 720) The above video is composed of stills from 2 orthogonal sets of 19 infinite sequences of mini-Mandelbrots in the Mandelbrot object. Each mini-Mandelbrot exists near the base of a branch coming off of a child bud of one of the main buds of the Mandelbrot object's central cardiod. Position, scale, orientation and color rate of each image have been adjusted so that the transitions appear as continuous as possible.

Of course it is never actually continuous. The branches coming off of a child bud can be two, three or four, but never three and a half. When one of the branches is decorated with a multi-arm spiral where the number of arms corresponds to the number of branches coming off of the parent bud, the number of arms may be five or six but never five and three quarters.

Each sequence rapidly approaches its limit without ever actually reaching it. Going 19 deep into a sequence a corresponding element in a neighboring sequence will appear quite similar. Jumping to that element, we follow the element's parallel sequence in reverse. Once we reach the first element in that sequence we jump to the first element in the next sequence, following the same pattern.

The last element of the last sequence in the current set of sequences is also the last element of the last sequence in the orthogonal set, so at that point we switch to the orthogonal set of sequences, taking it in reverse order until we reach the first element of the first sequences of both sets. Consequently the video is loopable.

In a certain sense, each infinite sequence is a discrete ("quantum") zoom sequence, where, just as a classic Mandelbrot zoom tends towards the point at a frame's center, these quantum zooms tend towards their Misiurewicz points, limits of quasi- self-similarity at the centers and tips of branches and spirals and cusps where buds join their parents. .

In this video we explore a two-dimensional field. However, the number of dimensions we choose to include is limited primarily by our imagination and the processing power of our machines.

Note: position, scale, orientation and color rates were calculated using Excel, individual frames were rendered by Fractal eXtreme, AVIs were created from the frames using VirtuablDub, AVIs were converted to MP4s using HandBreak, then MP4s were joined using MP4Tools.