The form of this lighting shade was derived from a phenomenon called Phyllotaxis, which governs the arrangement of petals and leaves in plants. Each petal is known to be positioned at a particular angle, called as the divergence angle, and a particular distance, which increases with a constant factor from the previous one creating a spiral lattice.
In a spiral lattice, the eye tends to connect nearest points into spirals. These spirals are called parastichies. There are two sets of parastichies winding in different directions and the number of parastichies in each set is always two consecutive numbers from a Fibonacci sequence.
This allows for creating various form by simple alterations in the variables that generate them.
The form was scripted in Processing and modeled in SolidWorks to create the shade using rapid prototyping.
The image below shows the snapshot of the processing sketch. And the sketch along with the code can be found here
Below are some images of the final form of the lamp shade.