i want to outline an iterative process that i perceive in plant development from the seed. This process i will attempt to lay out in the form of an algorithm.
I propose that the seed is a bounded region within which a recursive/iterative process is taking place. The process is stable within the boundary and forms patterns that are identified as structural regions within the boundary. These structural regions are expressions of "molecular" arrangement which themselves are expressions of "atomic" arrangement. Whatever these terms mean i perceive a self similarity demonstrated by magnification of any image taken of them.
Certain conditions destabilise the process within the boundary, either by crossing the boundary into the pattern and providing additional elements for the process to iterate on, or by providing an energy transfer at the boundary which "quickens" the internal iterative process,or both. The conditions that do this may also introduce new additional iterative processes to the existing boundarised ones so as to make a new recursive process which therefore has a new boundary organisation.
The iterative process has an input and output organisation and this is expressed structurally by process paths within the expressed pattern(s).
The new process develops its own boundary arrangements and so breaks through the existing boundary, which has degraded because the process that established it no longer is dominant. The new process has a boundary which reflects its structure, a input output iteration process which is dynamic and in replication and magnification mode.
The new process iterates through a certain undefined number of cycles each expressing a boundary that is self similar to the previous one and related by a multiplication and or magnification factor. Regions within that boundary are perceived at some level to be similar to the new boundary.
At an undefined number of cycles certain regions within the new boundary begin a perceivable miniturisation and or division process which begins to express structures that were within the originating seed. These regions are notable because of their variations in the boundaries, their size and the sheer number of miniature structures produced.
It is also notable that in producing these regions at miniature size the iterative process truncates and or stabilises. and this involves the loss out of the boundary of certain expressions of the process
After an undefined number of cycles the boundary in the miniaturisation regions become diminished and the seed like regions are lost to the main structure/ boundarised region. These seeds are capable of replicating this process in different but mostly nearby locations, and so develop the pattern on a macro scale.
The process within the subject boundary has developed at this stage a bi-polar dynamic which stabilises the rate of development of the boundary: The magnification/ multiplication aspect is counterbalanced by the miniaturisation/division aspect of the process or processes. Once it has reached this stage the iteration recycles through E, F, G, H indefinitely but at an altered rate dependent on this bipolar dynamic and the elements the process needs for its input processes.
The input output processes are a controlling dynamic system within the iterative process or proccesses and have not been fully realised in this algorithm at every stage. This again supplies levels of self similarity within the process which are output in a structure/ pattern which has similarity at several levels.
The computational aspects of this process could be said to reside in the molecular biological machines within the boundarised regions of a cell, but i prefer to locate them as properties of the space enfolded within those molecular structures.
If anyone can code this type of algorithm or has coded it , please respond, Also do play with modify or refine the algorithm as i know i will.
What interests me particularly about the shapes you obtained for the octahaedal shapes is the closeness in resemblance to the capsid of a particular type of virus. I wonder if you can produce a 3d image based around that form?
Of course the images are interesting and praiseworthy, but i feel i would if i had your skill attempt to explore some basic fundamental structures such as the chemical bonding arrangements say in the h2o complex, or carbon carbon bonds. I would also like some representation of M theoretic geometry in string theory. A tall order I know, but one can ask.
Lycium you have produced an interesting form but can you explain a little bit about which viral form inspired the image you have produced. I must say it does look nasty, but most viral forms look quite beautiful.
I am interested in the octahedral form and its relationship to the Koch snowflake. If you think about the H2O complex which forms at low temperatures the octahaedral form could represent the 2 oxygen atoms ands the 4 hydrogen atoms at the vertices:
O H H O
Now could this self assemble into the octahedral forms that you have depicted? Could the larger octahedrals have the form of a 3d serpinski gasket? If you could produce a form based around this, it would be interesting to see if it follows the natural forms of snowflakes.
Hello. I appreciate the comment about the quilting effect, but I also was very strongly reminded of the reptilian scale configuration on certain animals and the quilted effect in skin with pores in general. The spiral effect tends to give the image a feel of being around a crease in a fold of skin. Very interesting.