diatoms - california academy of sciences geology

1. Biddulphia deodora -  Miocene, ph#000058D,scale bar = 10 µm

2. Actinoptychus chenevierei - holotype, Cretaceous, ph#000677D, scale bar = 10 µm

3. Lithodesmium margaritaceum - Cretaceous, ph#000865D, scale bar = 10 µm

4. Aulacodiscus currus - holotype, Eocene, ph#001088D, scale bar = 10 µm

5. Triceratium diversum - holotype, Eocene, ph#001131D, scale bar = 10 µm

6. Triceratium swastika - Cretaceous, ph#000956D, scale bar = 10 µm

(Source: Flickr / casgeology)


“Phyllotactic Portrait of Fibonacci” by Robert Bosch

Mathematical artist Robert Bosch created this picture by adapting a well-known portrait of the Italian mathematician Leonardo Pisano Bigollo (c. 1170—1250), who was better known as Fibonacci.

Fibonacci described the sequence that bears his name in his 1202 book Liber Abaci, although the sequence was known to Indian mathematicians as early as the 6th century. The Fibonacci sequence begins 1, 1, 2, 3, 5, 8, 13, 21, the key property being that each of the terms from the third term onwards is the sum of the preceding two terms. 

Fibonacci used his sequence to study the growth of a population of rabbits, under idealising assumptions. The sequence can be used to model various biological phenomena, including the arrangement of leaves on a stem, which is known as phyllotaxis. Robert Bosch used a model of phyllotaxis to produce this picture. He explains:

Using a simple model of phyllotaxis (the process by which plant leaves or seeds are arranged on their stem), I positioned dots on a square canvas. By varying the radii of the dots, I made them resemble Fibonacci. Incidentally, the number of dots, 6765, is a Fibonacci number. So are the number of clockwise spirals (144) and counterclockwise spirals (233) formed by the dots. 

A framed version of this picture is currently being exhibited at the Bridges Exhibition at Gwacheon National Science Museum, Seoul. You can read more about the picture here: The same page discusses another version of the picture, also by Robert Bosch, but this time illustrating the Travelling Salesman problem. +Patrick Honner has posted about the other version of the picture here:

Relevant links

Robert Bosch’s website: 

Wikipedia on Leonardo Fibonacci:

The On-Line Encyclopedia of Integer Sequences on the Fibonacci numbers:

Fibonacci numbers in nature:

As well as featuring in this picture, the Fibonacci number 6765 is the name of an asteroid:

“We’re also a band.” (

(Found via +Patrick Honner.)

#art #artist #mathematics #scienceeveryday

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