The computer program Apex
Frank van der Linden, 2018

Around 1970, I began to recognize a particular quality of the phenomenon of plant pattern formation. More specific, about the sunflower head, I formulated this question: "How can I draw these spirals 'blind', so to say, without using continuous curves?". These curves were the result of a kind of interpretation. But I did not want to 'know' the Fibonacci numbers beforehand. It was just before the time that some people began to dream about the future, when every family would possess a computer, that I wrote a simple mathematical algorithm. In the eighties, I was both theory developing and computer modelling (in BASIC, in the MS-DOS environment on the so-called Enterprise computer). With the help of the mathematician Fred van der Blij and the biologist Aristid Lindenmayer, the Dislodgement Model was published in 1990, in Mathematical Biosciences.

I designed a new interface on the Commodore Amiga, a popular graphic computer of that time. Following the wise remarks of the biologist Konrad Bachmann, I developed the Stack-and-Drag Model - published 1996 in again Mathematical Biosciences. Exploring phyllotactic patterns for domeshaped buildings, I got my PhD in 1994. After computer program ApexD, I introduced ApexS. For the first time, a phyllotaxis generator for the entire - not bifurcated - plant body existed. It was necessairy now to choose between Apple and Windows. I chose the MS-Windows environment.
Being truly threedimensional, the theory had always been accompanied with a so-called 2.5D Visual Basic computer program. Now, I rewrote the software into the actual 3D Apex. Also, the two models were made accessible in one generator. In 2012, the program worked with OpenGL, with an accelaration in handling and growth simulations. In 2016 the first 3D-prints were made.

While many models are arising during the past decades, not one performs constructions for a complete phyllotactic pattern from seed to flower or composite - with all forms in between. Only Apex succeeds in this important task.
At the same time, Apex can be used for more than imitating expressions in Nature. It is a design tool with playing qualities. Playing, not with flying cars, but as a mental challenge, without the institutional and social bounderies of Science and Art. What parameters should I concider, and how is the relation of output with green natural structures?

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Apex - Development in the past and expectations for the future.