3D fractal art orchid flower generated using Apophysis 2.08 (3D Hack). I chose to model orchid flowers in Apophysis because their structure is unique among flowering plants. Orchid flowers exhibit bilateral symmetry as opposed to radial symmetry exhibited by most of the common flowers.
Each sepal was modeled by deformation of a hemisphere (3D primitive) using spherical and conic transform variations. The petals were a bit more challenging and were modeled by deformation of a hemisphere transform using small amounts of sinusoidal, spiral, conic, conic2, and xox transform variations. In a similar manner, the column was generated by deformation of a hemisphere transform using the julian3D transform variation, while the lip was generated using polar, conic, and flower2 transform variations. To summarize, each part of the flower was modeled through small deformations of a hemisphere transform using a variety of transform variations and post-transform modifications.
Here is a variation using linear transforms to generate additional orchids: