Here's an attempt to tie together a whole bunch of different threads from some recent videos both myself and some others have made. First up, e6 posted a video over the weekend about timing and direction where he pointed out the difficulties in making the traditional T&D combinations work with flowers that have an odd number of petals. In an odd bit of synchronicity, Justin Benson posted a video displaying an example of just that--wherein he takes a pentagram into split opposites by creating two pentagrams that reflect each other across a given axis. This reminded me of a paper Cyrille wrote a couple years ago, citing a side-effect of T&D combinations wherein they create different axes of symmetry and applied my own experiments with homogenous downbeat hybrids to work through all T&D combinations for two downbeat flowers and hybrids. This is a long one, I know, but I think it's a cool way of kind of working around this problem.

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techblog158.mp4