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# Ascending flowers Bloom zoetrope

\$169.60
3D printed in white nylon plastic polished to reveal a smooth matte finish.
QTY
##### Product Description
This sculpture is intended to be spun while iluminated by a strobe light flashing at just the right frequency.
It will then display flowers that ascend while blossoming. The flowers are fixed to spirals that seem to drift counterclockwise, and in a gorge on top there are wheels rolling slowly clockwise.

The video below shows a computer simulation of what it will look like.

The trick is that the angle through which the sculpture rotates between frames is the Golden angle. This is an idea by John Edmark: He took a sequence of shape elements, each rotated with respect to the previous one through the Golden angle about a common axis and also moving in the radial/axial plane, while possibly changing form. So after a rotation through the Golden angle, each element is replaced by its successor in the sequence, yielding an animation. This specific angle has the property of producing evenly spaced arrangements of elements because it is based on Ï†, the most irrational number.

With this design, I have expanded on the basic idea by also adding elements that repeat after a rational angle close to the golden angle. This works best if there is a Fibonacci number of these elements, because the ratio of successive Fibonacci numbers approximates the Golden section. The ratio fib(n)/fib(n+1) is smaller than the golden ratio if n is odd and larger if n is even. So A even-indexed Fibonacci number of elements will appear to be moving in a circle in the opposite direction of an odd-indexed Fibonacci number of elements. You can see this with the helical wires that hold the flowers and with the wheels on top.
So there are elements moving in three directions: left, right and up.

Help for building the electromechanical equipment required to animate the sculpture:
https://siquod.org/en/bloom
http://www.instructables.com/id/Blooming-Zoetrope-Sculptures/
##### Details
What's in the box:
Ascending flowers zoetrope
Dimensions:
13 x 13.01 x 11.56 cm
Switch to inches
5.12 x 5.12 x 4.55 inches
Switch to cm
Success Rate:
First To try.
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Rating:
Mature audiences only.