The computer program Apex
Frank van der Linden, 2020

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 produce these spirals 'blind', without drawing continuous curves?". In attempts to reconstruct phyllotactic patterns, I had to exclude Fibonacci or other numbers. These had to become possible output, not input!

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 a little computer called 'Enterprise'). With the help of the mathematician Fred van der Blij and the biologist Aristid Lindenmayer, the Dislodgement Model was published in Mathematical Biosciences, 1990.

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 (Mathematical Biosciences, 1996). Exploring phyllotactic patterns for dome shaped buildings, I got my PhD in 1994. My computer program ApexD changed into ApexS. For the first time, a phyllotaxis generator for the entire - not bifurcated - flowering plant body existed.

Being truly threedimensional, the theory had always been accompanied with a Visual Basic computer program in so-called 2.5D. Now, I rewrote it into 3D. Moreover, the two models were made accessible in one generator. In 2012, Apex used OpenGL, which accelarated handling and growth simulations dramatically. 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 is a design tool with playing qualities. Architects and structural engineers may develop towers and domes. Industrial designers may draw light sources, floor patterns, and puzzles. And playing can be done not with flying cars, but as a mental challenge, and without the institutional and social bounderies of Science and Art. Which parameters should I concider, how should I relate them, and how is the relation of output with green natural structures?

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Apex - arise, development, and expectations