Bada Bing Bada Bloom.

This is a flower.    fib

This is a bloom.    Animorphs-3D-printed-illusions-on-Instructables_dezeen_sq02

Blooms are based on a single number: 137.5º is a very special angle, called the golden angle, based on the golden ratio. When that angle is used by nature as a growth strategy, it leads to the formation of spiral patterns.

The spiral patterns that are recreated in the bloom are based on mathematics. These spirals are seen all across the world in nature. That is something that peeked our interest. To us, mathematics seemed like something detached from the natural world. Something very rigid and man-made. Seeing these patterns in nature was something that came as a shock to us and was the cause of our further exploration into the topic.

To begin, we went back to the basics of these spiral patterns. We researched a couple of mathematical explanations: The Fibonacci Sequence & The Golden Ratio.

The Fibonacci Sequence

The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth.

This sequence is essential to the spiral pattern because this is where the dimensions for the spiral come from. This can be seen below.

fibonacci sequenceUnknown

The numbers in the Fibonacci sequence are seen everywhere in nature from the way bunnies breed, to how many spirals there are on a pineapple, to how spiral galaxies are shaped!

The Rule for the sequence is xn = xn-1 + xn-2

Using the Fibonacci Sequence, we can actually move right into the next topic:

The Golden Ratio.

If we divide Fibonacci numbers (especially larger values), a peculiar thing occurs. There seems to be a limit. This can be seen below.

ratio of fibonacci numbers

1.618…….The Greeks called this PHI. We call it THE GOLDEN RATIO!

To prove that the limit of dividing Fibonacci numbers is in fact the Golden Ratio. We completed a proof seen below.

IMG_5173

This is all very important to the construction of a 3-D bloom. Remember… Blooms are based on a single number: 137.5º is a very special angle, called the golden angle, based on the golden ratio. When that angle is used by nature as a growth strategy, it leads to the formation of spiral patterns.

To construct a bloom, each petal must be strategically placed based on the golden angle, just like how they are made in nature!

When a strobe light is shone on the bloom as it spins, amazing affects can be seen as seen in the video below.

For our project, we 3-D printed a bloom in the innovations lab and created a turntable for it where speed could be adjusted. We then obtained a strobe light that had adjustable frequencies as an attempt to recreate the above effects. Below are some pictures of our project.

IMG_5246        IMG_5247

 

Bada Bing Bada Bloom.

Link to Presentation:

https://docs.google.com/presentation/d/1iDk9sS3IC450426fwezYpMhSPziRsuMaZxiqdvdJOWY/edit?usp=sharing

 

 

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