This lovely short film by Cristóbal Vila shows how the simple Fibonacci sequence manifests itself in natural forms like sunflowers, nautilus shells, and dragonfly wings.
See also Arthur Benjamin's TED Talk on the Fibonacci numbers and the golden ratio and the Fibonacci Shelf. (via @stevenstrogatz)
Tree Mountain is a man-made mountain 125 feet high covered in 11,000 trees planted in a configuration according to the Golden Ratio. This art installation was conceived and built by artist Agnes Denes in Finland and is designed to endure for 400 years.
A mountain needed to be built to design specifications, which by itself took over four years and was the restitution work of a mine that had destroyed the land through resource extraction. The process of bioremediation restores the land from resource extraction use to one in harmony with nature, in this case, the creation of a virgin forest. The planting of trees holds the land from erosion, enhances oxygen production and provides home for wildlife. This takes time and it is one of the reasons why Tree Mountain must remain undisturbed for centuries. The certificate the planters received are numbered and reach 400 years into the future as it takes that long for the ecosystem to establish itself. It is an inheritable document that connects the eleven thousand planters and their descendents reaching into millions, connected by their trees.
Here's Tree Mountain on Google Maps and a lovely video of the mountain shot from a drone:
You may have seen another of Denes' projects: a 2-acre wheat field she planted in 1982 near the World Trade Center in Manhattan.
(via shane)
Records of when the cherry blossoms appear in Kyoto date back 1200 years. (Let's boggle at this fact for a sec...) But as this chart of peak-bloom dates shows, since the most recent peak in 1829, the cherry blossoms have been arriving earlier and earlier in the year.
From its most recent peak in 1829, when full bloom could be expected to come on April 18th, the typical full-flowering date has drifted earlier and earlier. Since 1970, it has usually landed on April 7th. The cause is little mystery. In deciding when to show their shoots, cherry trees rely on temperatures in February and March. Yasuyuki Aono and Keiko Kazui, two Japanese scientists, have demonstrated that the full-blossom date for Kyoto's cherry trees can predict March temperatures to within 0.1°C. A warmer planet makes for warmer Marches.
Temperature and carbon-related charts like this one are clear portraits of the Industrial Revolution, right up there with oil paintings of the time. I also enjoyed the correction at the bottom of the piece:
An earlier version of this chart depicted cherry blossoms with six petals rather than five. This has been amended. Forgive us this botanical sin.
Gotta remember that flower petals are very often numbered according to the Fibonacci sequence.
If you spin these sculptures by artist John Edmark at a certain speed and light them with a strobe, they appear to animate in slowly trippy ways.
Blooms are 3-D printed sculptures designed to animate when spun under a strobe light. Unlike a 3D zoetrope, which animates a sequence of small changes to objects, a bloom animates as a single self-contained sculpture. The bloom's animation effect is achieved by progressive rotations of the golden ratio, phi (ϕ), the same ratio that nature employs to generate the spiral patterns we see in pinecones and sunflowers. The rotational speed and strobe rate of the bloom are synchronized so that one flash occurs every time the bloom turns 137.5º (the angular version of phi).
The effect seems computer generated (but obviously isn't) and is better than I anticipated. (via colossal)
Update: While not as visually smooth as his sculptures, Edmark's rotation of an artichoke under strobe lighting deftly demonstrates the geometric rules followed by plants when they grow.
Here we see an artichoke spinning while being videotaped at 24 frames-per-second with a very fast shutter speed (1/4000 sec). The rotation speed is chosen to cause the artichoke to rotate 137.5º — the golden angle — each time a frame is captured, thus creating the illusion that the leaves are moving up or down the surface of the artichoke. The reason this works is that the artichoke grows by producing new leaf one at a time, with each new leaf positioned 137.5º around the center from the previous leaves. So, in a sense, this video reiterates the artichoke's growth process.
(via @waxpancake)
Update: This similar sculpture by Takeshi Murata is quite impressive as well.
(via @kevmaguire)
The Fibonacci Shelf by designer Peng Wang might not be the most functional piece of furniture, but I still want one.
The design of the shelf is based on the Fibonacci sequence of numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, ...), which is related to the Golden Rectangle. When assembled, the Fibonacci Shelf resembles a series of Golden Rectangles partitioned into squares. (via ignant)
If you divide 1 by 999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 (that's 999 quattuordecillion btw), the Fibonacci sequence neatly pops out. MATH FTW!
At the end of Carl Sagan's Contact (spoilers!), the aliens give Ellie a hint about something hidden deep in the digits of π. After a long search, a circle made from a sequence of 1s and 0s is found, providing evidence that intelligence was built into the fabric of the Universe. I don't know if this Fibonacci division thing is on quite the same level, but it might bake your noodle if you think about it too hard. (via @stevenstrogatz)
Update: From svat at Hacker News, an explanation of the magic behind the math.
It's actually easier to understand if you work backwards and arrive at the expression yourself, by asking yourself: "If I wanted the number that starts like 0.0...000 0...001 0...001 0...002 0...003 0...005 0...008 ... (with each block being 24 digits long), how would I express that number?"
(thx, taylor)
