Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

UA Mathematicians Predict Patterns in Fingerprints, Cacti

02.04.2004


Img 1 (above): Human fingerprint patterns are created because basal skin grows faster than surface skin, which then buckles, forming ridges .
Img 2 (below): Kuecken developed a mathematical model that can reproduce fingerprint patterns, like this one.


Shipman found that cactus stickers predicatably align in spiral patterns


Patterns in nature can be seen every day, yet in many cases, little is understood about how and why they form. Now University of Arizona mathematicians have found a way to predict natural patterns, including fingerprints and the spirals seen in cacti.

UA graduate student Michael Kuecken developed a mathematical model that can reproduce fingerprint patterns, while UA graduate student Patrick Shipman created a mathematical model to explain the arrangement of repeated units in various plants. Shipman’s report on his work will be published in an upcoming issue of Physical Review Letters.

Even though the use of fingerprints for identification began more than 2000 years ago in China and they have been studied experimentally for over two hundred years, there is no widely accepted explanation for their occurrence. Likewise, the reasons behind nature’s choice of patterns in plants have been difficult for mathematicians to explain, despite these patterns having been identified centuries ago.



“What I like about this research is the interplay between math and biology. It is actually quite difficult, because the disciplines require a somewhat different mindset and biology is notoriously bewildering and full of detail,” Kuecken said. “In a way, dealing with this problem was like putting together a jigsaw puzzle of facts. I had to try out different things and could use math, and sometimes common sense, to see if the pieces actually fit.”

Human skin has multiple layers, including the outermost epidermis and the inner dermis. The outer and inner layers are separated by the basal layer, which is composed of cells that constantly divide. Growth occurs in a similar fashion in plants, which have areas of continuous cell growth, such as the tip of a cactus, that allow the plant to grow larger.

The basal layer in human skin and the equivalent layer in plant skin grow at a faster rate than either the surface layers or the thick dermis layer. As the basal layer continues to grow, pressure increases. In both plants and fingertips, the growing layer buckles inward toward the softer inner layer of tissue, relieving the stress. As a result, ridges are formed on the surface.

The undulations from the buckling form fingerprints and various patterns in plants, from the ridges in saguaro cacti to the hexagons in pineapples. The way a pattern is formed, regardless whether it is a fingerprint or a plant, is related to the forces imposed during ridge formation.

The basic properties responsible for the mechanism of buckling in plants and fingerprints happen in other materials as well. Kuecken and Shipman’s graduate advisor, UA professor of mathematics Alan Newell, said, “In material science, high-temperature superconductors seem to be connected with stresses that compress to build the structures in various high-temperature materials. Indeed, the idea that buckling and surface stresses would have something to do with the patterns you see in plants is fairly recent.”

In fingerprints, ridge formation is influenced by discrete elevations of the skin on the fingertips, called volar pads, which first appear in human embryos at about six and a half weeks. The volar pads’ location is where the epidermal ridges for fingerprints will arise later in development.

Kuecken explained that as the volar pads shrink, it places stress on the skin layers. The ridges then form perpendicular to this stress. There are three basic patterns of fingerprints known as arches, loops and whorls that form in response to the different directions of stress caused by shrinking of the volar pads. Other research on ridge formation has already shown that if a person has a high, rounded volar pad, they will end up with a whorl pattern. Kuecken’s mathematical model was able to reproduce these large patterns, as well as the little intricacies that make an individual fingerprint unique.

Shipman’s model, like Kuecken’s, also took into account stresses that influenced ridge formation. In plants, forces acting in multiple directions result in complex patterns. For example, when buckling occurs in three different directions, all three ridges will appear together and form a hexagonal pattern.

“I’ve looked at cacti all my life, I really like them, and I’d really like to understand them,” Shipman said. To study these patterns, Shipman looked at the stickers on a cactus or florets on a flower.

When a line is drawn from sticker to sticker on a cactus in a clockwise or in a counterclockwise direction, the line ends up spiraling around the plant. This occurs in many plants, including pineapples and cauliflower. When these spirals are counted, it results in numbers that belong to the Fibonacci sequence, a series of numbers that appears frequently when scientists and mathematicians analyze natural patterns.
Shipman found that cactus stickers predicatably align in spiral patterns.

From his model, Shipman found that the initial curvature of a plant near its growth tip influences whether it will form ridges or hexagons. He found that plants with a flat top, or less curved top, such as saguaro cacti, will always form ridges and tend not to have Fibonacci sequences. Plants that have a high degree of curvature will produce hexagonal configurations, such as those in pinecones, and the number of spirals will always be numbers in the Fibonacci sequence.

Newell says that Shipman’s mathematical model demonstrates that the shapes chosen by nature are those that take the least energy to make. “Of all possible shapes you can have, what nature picked minimizes the energy in the plant.”

Alan C. Newell | University of Arizona
Further information:
http://uanews.org/cgi-bin/WebObjects/UANews.woa/wa/SRStoryDetails?ArticleID=8920

More articles from Physics and Astronomy:

nachricht Graphene and quantum dots put in motion a CMOS-integrated camera that can see the invisible
30.05.2017 | ICFO-The Institute of Photonic Sciences

nachricht New Method of Characterizing Graphene
30.05.2017 | Universität Basel

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: New Method of Characterizing Graphene

Scientists have developed a new method of characterizing graphene’s properties without applying disruptive electrical contacts, allowing them to investigate both the resistance and quantum capacitance of graphene and other two-dimensional materials. Researchers from the Swiss Nanoscience Institute and the University of Basel’s Department of Physics reported their findings in the journal Physical Review Applied.

Graphene consists of a single layer of carbon atoms. It is transparent, harder than diamond and stronger than steel, yet flexible, and a significantly better...

Im Focus: Strathclyde-led research develops world's highest gain high-power laser amplifier

The world's highest gain high power laser amplifier - by many orders of magnitude - has been developed in research led at the University of Strathclyde.

The researchers demonstrated the feasibility of using plasma to amplify short laser pulses of picojoule-level energy up to 100 millijoules, which is a 'gain'...

Im Focus: Can the immune system be boosted against Staphylococcus aureus by delivery of messenger RNA?

Staphylococcus aureus is a feared pathogen (MRSA, multi-resistant S. aureus) due to frequent resistances against many antibiotics, especially in hospital infections. Researchers at the Paul-Ehrlich-Institut have identified immunological processes that prevent a successful immune response directed against the pathogenic agent. The delivery of bacterial proteins with RNA adjuvant or messenger RNA (mRNA) into immune cells allows the re-direction of the immune response towards an active defense against S. aureus. This could be of significant importance for the development of an effective vaccine. PLOS Pathogens has published these research results online on 25 May 2017.

Staphylococcus aureus (S. aureus) is a bacterium that colonizes by far more than half of the skin and the mucosa of adults, usually without causing infections....

Im Focus: A quantum walk of photons

Physicists from the University of Würzburg are capable of generating identical looking single light particles at the push of a button. Two new studies now demonstrate the potential this method holds.

The quantum computer has fuelled the imagination of scientists for decades: It is based on fundamentally different phenomena than a conventional computer....

Im Focus: Turmoil in sluggish electrons’ existence

An international team of physicists has monitored the scattering behaviour of electrons in a non-conducting material in real-time. Their insights could be beneficial for radiotherapy.

We can refer to electrons in non-conducting materials as ‘sluggish’. Typically, they remain fixed in a location, deep inside an atomic composite. It is hence...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Marine Conservation: IASS Contributes to UN Ocean Conference in New York on 5-9 June

24.05.2017 | Event News

AWK Aachen Machine Tool Colloquium 2017: Internet of Production for Agile Enterprises

23.05.2017 | Event News

Dortmund MST Conference presents Individualized Healthcare Solutions with micro and nanotechnology

22.05.2017 | Event News

 
Latest News

3D printer inks from the woods

30.05.2017 | Life Sciences

How circadian clocks communicate with each other

30.05.2017 | Life Sciences

Graphene and quantum dots put in motion a CMOS-integrated camera that can see the invisible

30.05.2017 | Physics and Astronomy

VideoLinks
B2B-VideoLinks
More VideoLinks >>>