This is an idea for a skyscraper based on spiral phyllotaxis, like the sunflower system, that exhibits spiral pods always in Fibonacci numbers.
A branching system of five ‘leafs’ grows around the ‘trunk’ and fold out to provide sun light protection. The folding part is also meant to have solar panels on it. In one of the stages, each level (a set of five) grows at 45 degrees, so that, they complete a whole round every eight levels.
Departing from another approach, I developed a script that generates a set of points in consecutive rings that get bigger in a golden ratio and are joined by polylines following emergent spiral patterns of those points. This forms a sort of a radial diagrid that resembles a stem cell structure and is being used as the internal structure of the tower. This structure also turns while grows, but this time, since is using inclined columns at the interior as well, the inclination angle is restricted to meet usability issues. The last animation shows the growth system implemented in Grasshopper.