How were the “digital orchid flowers” generated?
Digital orchid flowers were 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 digital orchid flowers:
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What are fractals?
In mathematics, a fractal is a self-similar subset of Euclidean space whose fractal dimension strictly exceeds its topological dimension. Fractals appear the same at different levels, as illustrated in successive magnifications of the Mandelbrot set; because of this, fractals are encountered ubiquitously in nature.
Fractals exhibit similar patterns at increasingly small scales called self similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, it is called affine self-similar.Wikipedia