Let’s End Poaching Before It’s Too Late!

posted in: Art. Nature. Technology | 0

“Plans to protect air and water, wilderness and wildlife are in fact plans to protect man.” ~ Stewart Udall

Let’s End Poaching Before It’s Too Late: A Conversation with Mr. Tom Tochterman, Founder of Rhino Mercy

At the turn of the 19th century there were an estimated one million Rhinos in Africa; today there are less than 30,000. Since beginning of 2014, 1,173 Rhino’s have been slaughtered in South Africa. Rhino’s are drugged so they can’t move, but they still hear, smell, and feel everything, while their horn is chopped by an axe. And why? Simply for a horn that is nothing more than a keratin compound that has no medical value with most recent use for preventing hangovers from drinking alcohol! This is 2014, humans should be smarter than believing in myths that did not even exists in the pre-historic ages! Rhinos are intelligent, social, emotional animals and can feel pain just like humans. If things remain the same, your newborn children will no longer see a Rhino. The technology and resources wildlife conservation groups need to stop this is nothing sci-fi like. The technology they need is already developed and has been used in other applications. We need to act now and do whatever it takes to use our expertise and resources to save the last Rhinos!

If we don’t act now to save the Rhinos, the rest of wildlife from elephants, tigers, lions and many more are doomed.  We need awareness and immediate action from individuals of all backgrounds, artists, scientists, engineers, historians, entrepreneurs, film producers, inventors , and world leaders and policy makers to take your expertise to help save the remaining Rhinos. It’s still possible to save them by educating the world, allocating necessary resources, adjusting policies, and the use of existing technologies, but we need to act NOW.

I had the opportunity to interview Mr. Tom Tochterman, Founder of Rhino Mercy. Rhino Mercy in partnership with a South African/UK organization Transfrontier Africa is implementing actions to save the remaining rhinos. Here  are Tom’s valuable insights on the history of African Rhinos, what is happening to them, current strategic initiatives and actions being taken to save the Rhinos, technologies such as Drones, RFID, Camera traps being used; and additional technologies and resources needed that can help save Rhinos; and most importantly ACTIONS by the individuals pleading to the governmental levels that can help  save Rhino’s NOW!

Can you tell me a little about Rhino Mercy?

Though our work began in 2011, Rhino Mercy was formally established in January of 2012 in response to the escalating and brutal nature of rhino poaching in the Republic of South Africa. RM is a US based non-profit tax exempt 501c3 corporation with no paid employees. We have four main strategic objectives which are; 1) provide support for anti-poaching units (boots on the ground), 2) explore the use of technology in anti-poaching initiatives (ie. vhf/gps collars, horn infusion, and drones), 3) create rhino ambassador through voluntourism opportunities, and 4) academic research. Our vision, mission, key objectives, core values, and key initiatives are all listed on our website at www.rhinomercy.org Rhino Mercy has partnered with a South African/UK organization Transfrontier Africa whose director (Craig Spencer) is also the Head Warden of the Balule Nature Reserve and Olifants West Nature Reserve, a 100,000 acre private reserve which is part of the Greater Kruger National Park.

Can you tell me about the history of African Rhinos and what is happening to the them now?

Nearly all of the sub-species of African rhino’s are extinct, extinct in the wild, or critically endangered per the Convention on International Trade of Endangered Species (CITES) and the International Union Conservation Nature (IUCN). At the turn of the 19th century there were an estimated one million rhino of various subspecies roaming on the African continent; today there are less than 30,000 (the actual number some estimate to be approximately half that amount) which breaks down to approximately 5,000 African Black Rhino (half located in the Republic of South Africa) and 25,000 Southern White Rhino (approximately 80% located in the Republic of South Africa). The Southern White Rhino was nearly extinct by the 1970’s but brought back from the brink and until recently was continuing to recruit at a positive rate. Some believe that at the current rate of poaching, natural mortalities, stock sales/professional hunts that the species is in a negative growth rate and in danger once again. The Southern White Rhino is legally classified as “Appendix II, threatened” and the African Black Rhino is classified as “Appendix I, critically endangered IUCN red listed”.

The numbers are devastating, the latest report shows since beginning of 2014, 1030 rhino’s have been slaughtered in South Africa. Can you explain why and how the Rhino’s are killed?

Sadly, as of this writing the number of rhino’s poached in South Africa stands at 1,173 which does not include calves, unborn calves, or carcasses that have not been found. It is anticipated the official number will exceed 1,200 by the end of the year. How the rhino’s are killed is probably what motivated me the most to get involved in this war (and war it is). Often times poachers will dart the rhino in the cover of dark nights aided by the poacher’s moon (full moon) with a drug called M99. The drug only immobilizes the animal meaning its sensory functions are operating at full strength; the rhino hears, smells, and feels everything, it just can’t move. Once the animal is down the butchers take an axe the front of the rhino’s face chopping into the skull to remove every part of the horn they can. Often we find the carcass with machete slashes across its spine above the rear legs indicating the rhino was able to move because not enough M99 was injected. On the black market rhino horn is reported to sell for USD $70,000 to $90,000 per kilo; there are on average four kilos of horn per rhino. Keep in mind, the horn is a keratin compound with no medicinal value. The most recent known purpose for consumption is as a supplement to prevent hangovers from drinking alcohol! Nearly all consumption/demand comes from Southeast Asia. The profile and sophistication of the poacher is varied, some are highly armed and skilled ex military from Mozambique with helicopters while others are home grown from edge communities to the national parks with homemade guns. The criminal networks have been found to include people at all levels in government, veterinarians, game rangers, park employees, pseudo hunters, lodge staff, etc….

If nothing is changed, what is the expected time frame Rhino’s will be extinct?

How do you think the loss of Rhino’s could impact tourism and the economy? The question of when extinction will occur is a one that is difficult to answer because the government did not finish its last rhino census. Some people say it’s because the numbers may be much lower than the government wants to admit. There are certainly statistical formulas that can accurately predict extinction but they require critical data that is not available. The numbers provided by the government are considered suspect. Everyone does seem to agree that the ecotourism industry would be substantially harmed if the Big Five is reduced to the Big Four. Losing an “umbrella” or “high value” species would be the sign of much worse times to come as the elephant and lion are undoubtedly just as threatened. One elephant is poached across Africa every 15 minutes and now that Tigers are nearly extinct Traditional Chinese Medicine doctors are saying that lion bones and parts are a suitable substitute! If we cannot save the rhino, the rest are doomed in my humble opinion. The rhino wars are ground zero for sub-Saharan Africa.

What are your initiatives and action plans to save the remaining Rhino’s? 

Our main strategic initiative is called the Balule Rhino Conservation Project (a pdf copy of the project is posted on our website for download). The project is essentially a multifaceted approach to the crisis from an enforcement approach and social development approach. In brief, we have armed guards and unarmed environmental monitors patrolling the Balule Reserve aided by real time and near real time rhino data. The social development initiative involved the creation of the first ever South African female anti-poaching unit called the Black Mamba’s (an extremely lethal snake in the bush). We recruited women in their 20’s from local communities and provided them training, equipment, housing, food rations, and salaries. This program is a partnership that includes SANParks (South African National Parks). The Black Mamba program is expected to elevate the paradigm of women in the workforce and specifically women in conservation. It is our opinion that women are the educators and nurturers in their communities and that they will return to their villages on their leave cycles and express to others that they are making a living protecting the environment therefore it becomes an important cultural value with both the new generation and the old guard. Noteworthy is that we have had very little turnover among the women and we are approaching a one year anniversary while we have had very high turnover among the men. Also interesting is that we have not had a rhino poached in nearly eight months but on reserves surrounding us they are dropping like flies. We are currently the only game reserve to have the Black Mamba or similar program in operation but we have recently been asked to train 19 additional women for a bordering reserve! We have high hopes for this program and firmly believe in the social development aspect of conservation.

What and how are some of the existing technologies such as drones used to save the Rhino’s?

We field tested drones in 2013 and ultimately found them to be too costly in terms of initial capital requirements as well as ongoing maintenance. Drones could be a high value asset in tracking poachers once they have been detected. Within days of the drone demonstration one of our cellular enabled camera traps transmitted pictures of three poachers with guns to the phone of the head warden; it took a tactical unit more than an hour to get to the initial location and by that time the poachers disappeared into the bush. If our staff would have deployed a drone we had the ability to track them while the tactical unit was enroute. Our current use of technology focuses on RFID tags and tracking collars/software for location and general spatial data. We also rely on day/night camera traps; not cellular enabled as data fees are cost prohibitive (we are exploring the development of a private network to solve the data cost issue). All technology comes at a high cost in initial outlay, maintenance, and operations. For example, one would think camera traps to be a simple cheap tool however that is far from the truth, camera traps are very susceptible to being destroyed by animals, data cards can be filled quickly by curious Vervet Monkeys, batteries need to be replaced often, and the wear and tear on vehicles to service dozens of camera traps is very expensive and time consuming. Further complicating matters is the extremely harsh natural environment of the bush; the extreme seasonal heat, rain, and humidity take their toll on everything and everybody.

Since time is so valuable as everyday more Rhino’s are being slaughtered, what can everyday people do NOW to save the Rhino’s?

Simply donate their time, treasure, or talent to organizations they investigate and confirm to be valid. I am often asked how to know the good guys from the bad and my standard answer is that they (the potential donor) ask for the financial statements from an organization they are interested in and check to see if they are spending money on things that matter to them (the donor). If they won’t provide financial statements then walk away. Financial statements of US non-profits are a matter of public record and should never be denied. There are likely as many environmental scams tapping into this crisis as there are genuine organizations in the fight so caution is advised. Also, I highly recommend people get educated on harmful consumptive behaviour as it relates to natural environments and engage the government and local communities on the issue of extinction and ecosystem degradation.

Are there organizations that have meetings open to the general public to attend?

In order to effectively engage with expertise one must ultimately immerse with role players. In my case, I recognized a problem, immersed myself in social media to determine who the role players were, reached out to the role players for private face to face meetings, became known as an interested party through professional associations, then contributed my time, treasure, and talent to the cause and became one of the role players (according to others). Social media is playing an amazing role as a catalyst for people around the world. I cannot tell you how many good people I have first met in the virtual world that have turned out to be true blue. If one cannot do it like I did, for face to face kinds of interactions, local zoo’s or environmental groups might be a good start in general for finding working groups. The US Fish and Wildlife Service also has a pretty good website for different kinds of opportunities.

If we had no limits in technological capabilities in an imaginary world, what are some technologies that would be on your wish list to help?

A time machine! Seriously though, there are two parts to the equation that have very different needs. First the demand side, which I am not involved with but understand that technology is very critical in effective messaging for demand reduction campaigns. The second part of the equation is the supply side which I am engaged with. I believe ultimately if we find a way to completely devalue the market price of the horn the problem of poaching goes away. My first wish would be for an effective technological process that could be applied to the rhino horn rendering the horn zero commercial value. Rhino horn infusions currently conducted by an organization called Rhino Rescue Project have been very successful but have also met with strong criticism. The infusion process which I completely support may not be perfect but it is one that is headed in the right direction and may well prove to be the ultimate tool. My second wish would be to provide better and more equipment to the rangers in the field such as night scopes and binoculars, drones with state of the art night time cameras and animal detection software, radio’s, and a secure private network for transmitting unlimited data and images. Third would be to provide military grade “rugged” laptops to our four staff members to greatly enhance internal communications. The laptops we currently use are not specified for the harsh conditions of the African bush and are often unreliable and a drain on limited resources. Fourth would be a variety of networked detection sensors strategically placed around the reserve for early detection of intrusions. Finally, a fully funded state of the art helicopter with night detection capabilities would help immensely in responding to immediate poaching threats and to aid in the maintenance of existing rhino ankle collars and snare removal operations. Currently we hire a helicopter and pilot on an as needed basis but it is a budget breaker!

Anything else you would like to add?

An important aspect of our collective efforts to save the rhino from extinction comes from the politics of conservation. There is one single issue that has become terribly divisive among conservationists and that is trade. Currently international law prohibits the international trade of rhino horn and domestic law prohibits the domestic trade of rhino horn within South Africa. Some believe that opening trade might reduce the rate of poaching but a closer look reveals something very different. Poaching has increased exponentially over the last few years after the announcement from the South African government that it intends to request a lifting of the international ban at the next CITES meeting in 2016. Rhino Mercy’s position is that any attempt to encourage consumption will lead to an increase in demand and therefore further harm the species. Even if trade were allowed under a highly regulated system there is no incentive for the beneficiaries of trade to flood the market in order to bring the price down. It is further recognized that even if the market could be flooded it could not be sustained. Similar promises were made in establishing the Kimberly process for controlling blood diamonds which has failed to achieve its goals. Even “once off” sales of stockpiles is dangerous as has been the case with ivory in East Africa where poaching of elephants skyrocketed after the once off sales closed. My general view is that while I support market economic theory in general, it has contributed to our environmental problems in several ways but specifically by ignoring the intrinsic values of ecosystems and natural resources in complete favor of their extrinsic values. This we must change.

Ant Colony: Inspiration for algorithms shaping the future from mathematics to robotics and self-driving cars

posted in: Art. Nature. Technology | 0

Emergent behavior in complex adaptive Ant colony: Inspiration for algorithms from mathematics to robotics and self-driving cars.

Many of us view ants as useless and annoying insects. Once you observe and study the behavior of ants you will see they are one of the most fascinating and collectively efficient, adaptive, and smart creatures; and modeling their behavior can lead to science fiction like world changing discoveries and innovations in a multitude of applications.

Some ants can carry over 100 times their own body weight and change the size and shape of the pads on their feet depending on the load they are carrying. Astonishing behaviors emerge from collective groups of ants interacting with each other and the environment.

Studies aimed at understanding and modeling the behavior of ants and other insects and species such as fish and birds can provide inspiration for the development of algorithms for solving difficult mathematical and computational problems. Some applications include network routing, robotics, and urban transportation systems. Imagine groups of robots that can communicate with each other to achieve a certain goal, adapt to the environment, and change their shape depending on the environment, whether they have to run, jump, swim, fly, or walk!

More than 10,000 known ant species exist around the world. Ants are adaptive and social creatures, they communicate by using chemicals known as pheromones that can alert others of danger or lead them to a food source. One ant by itself is not smart, however, when you have a group of ants interacting with each other and the environment, complex outcome is produced. This is a phenomenon known as Emergence. In addition, Stigmergy occurs when elements of the system interact indirectly through the environment. This behavior is also known as Swarm Intelligence, it consist typically of a population of simple agents interacting locally with one another and with their environment.

Imagine if we could mimic this behavior by developing a swarm of self-organized adaptable robots, sensors, connected objects that can be released to accomplish specific tasks, search and discover the physical space, be used for search and rescue, and wildlife conservation initiatives, or a swarm of driverless cars autonomously finding the shortest path for their routes!

In summary, studies of ants’ behavior have shown that: Ants drop pheromones as they move.   Ants have preference to follow high pheromone trails. More pheromones will accumulate on the shortest path.  Ants use stigmergy to find the shortest path between home and food. Pheromone deposit left by ants manifests stigmergy. When ants face an obstacle between nest and food  they choose to turn left or right with equal probabilities.  After some time period all ants have chosen the shorter path.

In grad school, I became fascinated with Artificial Intelligence and decided to research Ant Colony Optimization for my theses. I used an algorithmic approach to simulate ant colony behavior and focused on the Stigmergic Emergent behavior in complex adaptive ant colony.

I experimented with interactions of multiple parameters including multiple food sources, obstructions, two types of pheromones, and use of full grid.

Parameters of the model:

    • Number of ants
    • Grid size
    • Ant’s pheromone level and pheromone capacity
    • Pheromone capacity and level are changed by the same multiple.
    • Single vs. multiple food source.
    • Distance between food and home
    • No obstruction versus obstructions


Some questions that I addressed:

Does it help to have more ants? How many ants is enough?  Should ants have large stores of pheromones for their travel or is it better for them to have small stores? What factors must be adjusted when the distance between home and food changes? What is affected when obstructions are introduced into the grid?


Simulation Findings: If one parameter of the model changes, we can produce stigmergic behavior by making some appropriate changes in the values of other parameters.

  • The environmental factors, such as, place of food, place of home, obstructions, single or multiple food sources, or the grid size affect behavior, but they are not the determining factors.
  • Internal variables are the determining factors.
  • Pheromone capacity and the number of ants are internal determining variables.
  • Distance between home and food is the most important environmental variable.
  • As the home-food distance increases, both the pheromone capacity and the number of ants must be increased to achieve convergence to stigmergic behavior.
  • For each value of the home-food distance there is a minimum pheromone capacity that could lead to convergence.
  • Although more ants are required when the distance increases, no specific mathematical   formula between distance and number of ants was observed.
  • For each distance multiple, a minimum threshold for the number of ants is required for convergence.


UCI Beall Center for Art + Technology

UCI Beall Center for Art + Technology

posted in: Art. Nature. Technology | 0

A conversation with Samantha Younghans-Haug, Program Director at University of California Irvine Beall Center for Art + Technology.

Interactive Art that uses different forms of science and technology to engage the senses; collaborations among artists, scientists and technologists to spark new ideas and discoveries….


I had the opportunity for a Q&A with Samantha Younghans-Haug, Program Director at the Beall Center for Art + Technology.


1- Can you tell me a little about the UCI Beall Center and what you do at the UCI Beall Center? 

The Beall Center promotes new forms of creative expression by: exhibiting art that uses different forms of science and technology to engage the senses; building innovative scholarly relationships and community collaborations between artists, scientists and technologists; encouraging research and development of art forms that can affect the future; reintroducing artistic and creative thinking into STEAM (Science, Technology, Engineering, Arts, and Math) integrated learning in K-12 to Higher Education.I am the programs director at the Beall Center, and really handle just about anything and everything that comes my way – from developing & collaborating on new programs such as our new middle and high school Expressive Robotics Camp, and putting on events such as Family Days, lectures, workshops & openings, to figuring out how to trouble-shoot technology issues, working with exhibition installers and artists, training docents, editing exhibition catalogs, writing grants and putting together marketing materials both printed and online, writing press releases, and of course managing all the day to day business that happens. I work closely with and have learned a lot from my colleague and friend David Familian who is the curator and Artistic Director of the Beall. I am also involved in STEAM education initiatives and work with individuals on a county and national level, and am a contributor to the developments around the OC Mini Maker Faire.


2- What inspired you to start the Beall Center?

The Beall Center first opened its doors in 2000, years before I began which was in 2006.  The Beall Center received its initial support from the Rockwell Corporation in honor of retired chairman Don Beall and his wife, Joan, the core idea being to merge their lifelong passions – technology, business and the arts – in one place.  Here is a link to learn more about Don Beall:  http://merage.uci.edu/ResearchAndCenters/Beall/Meet-Don-Beall.aspx


3- What type of community programs and events do you have at the Beall Center?

Family Day is our most popular community event and is offered twice a year in conjunction with each exhibition.  Typical Family Days provide demonstrations by local companies in manufacturing, programming, engineering, optics, arts and design. I try to bring together an eclectic grouping of individuals from around the community and from various colleges and universities.  In addition I like to invite young adults (or individuals of any age) who are excited about something they’ve made to come and demonstrate or show off their work.  We have an active student body involved in various clubs from DIY clubs and computer programming/hackers to poetry and music clubs, and it is always fun to have them participate in Family Day, when they are available.  I also typically have a wonderful group of volunteers from the UCI school of Education participating, and of course our wonderful Beall Docent staff.  I believe that Family Day presents a unique learning experience not only for our visitors, but also for our UCI students and participants.  I’ve seen a lot of networking and new projects come out of Family Day.We also provide our new Expressive Robotics camp that emphasizes programming expressive & responsive movement, and we offer all levels of tours from elementary to college level to senior groups.  Tours are sometimes matched with lectures and simple hands-on art and tech projects.


4- What type of exhibitions do you hold at the Beall Center? What makes an exhibition most interesting? Can you describe one of the past exhibitions that was most inspirational to you?

Every exhibit at the Beall is different and all are inspiring to me in many ways.  Just check out the past exhibitions listed on our website.  It really amazes me the works that people envision and produce.  One of my favorite exhibits was Paul Vanouse’s “Evidence” (Feb 2013).  The exhibit included his work titled “Latent Figure Protocol”, a performative biological media installation that used DNA samples to create emergent representational images. The installation was a live scientific experiment employing a reactive gel and electrical current that produced images that relate directly to the DNA samples used. The Docents and I would “perform” the experiments every 3 days throughout the exhibition, with each image slowly fading to nothing by day 3.  Not having any personal experience with the sciences, it was really exciting working with this new art medium (DNA!).  (http://beallcenter.uci.edu/exhibitions/evidence-works-paul-vanouse)The other exhibit that was really one of the most interesting and inspirational to me was “EX-I-09” (April 2009) by artist Shih Chieh Huang (CJ).  I am interested in kinetic works (either interactive, responsive or…) that create new and unusual environments, and I am also very interested in the repurposing of materials – and this was CJ.  Amazing, work!  It made me want to go out and start making things. (http://beallcenter.uci.edu/exhibitions/ex-i-09)


5- How do you think the concept of Art + Technology has evolved in the community since the start of the Beall Center? How do you think better understanding of the connections between Art and Technology will help shape new forms of creations and disruptive technologies?

The Beall Center provides a unique space in our community to see the convergent works of collaborating artists and technologists.  We hope that people come to the Beall, interact with the works & space, and leave imagining new things, and inspired to create and innovate.  Being tucked away on a campus makes it hard for the community to discover the Beall, and so we have our challenges.  I believe our community events help us tremendously to get the word out.  We always ask that when people come to the Beall Center that they always come back with a new person and that person comes back with a new person, and so on and so on.  A lot of our visitors arrive either by word of mouth or by chance discover or just stumble in lost on campus (those visitors are always fun).  We would really like to be brighter on the radar of art & tech, and we believe that over the past few years this is happening more and more.  We were recently awarded a grant from the Andy Warhol Foundation for the Visual Arts.  Successes like that help put us on the forefront.I believe that as our culture and society continues to evolve and change with or because of technology that it is even more important to stimulate imagination to advance creativity and innovation.  There has been a big push for STEM education, and I believe that the arts in all its wonderful forms (fine arts, crafts, dance, music, design, prose & poetry, lyrics & language) must also be included and valued just as importantly, otherwise we will continue with the same paths.  I believe using our imaginations to become creative causes us to care and causes us to change our way of thinking and then opens us up to so many possibilities. Arts+STEM or STEAM, or whatever anyone wants to call it is important in all its varied forms (individual disciplines, multi/inter/trans-disciplinary, etc.).  I also believe that collaborations among artists, scientists and technologists bring about new ideas and discoveries.  When people work together and combine their research and practices amazing things can happen.  Often engineers think differently them artists, neither is better, but together they experience in different ways and can learn from one another.  Okay, just getting a little too philosophical here…


6- Anything else you would like to add?

I didn’t come to this position at the Beall as an art and technology person.  My background was twofold & separate – art and business.  I’ve learned a lot being here, and I am extremely thankful for the many different people I’ve come to know and learn from over the years.


Mathematics in Nature and in Art

posted in: Art. Nature. Technology | 1

From paintings and monuments inspired by mathematics of nature, to complicated and beautiful shapes created from simple math equations

The tight connection between Art and Mathematics is fascinating ; they have had a long historical relationship dating back to 2,560 BC. From artists and architects inspired by mathematics in creating their paintings and monuments, to mathematicians developing mathematical models which result in amazing complex patterns and designs.

“The universe is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures. Artists who strive and seek to study nature must therefore first fully understand mathematics. On the other hand, mathematicians have sought to interpret and analyze art through the lens of geometry and rationality. ” – Galileo Galilei


Going back in history, evidence of mathematics influence has been seen as far back as 2,560 BC; in monuments such as the Great Pyramids and the Coliseum. Also, painters and philosophers observed geometric shapes and patterns in nature and made use of mathematics in their work; incorporation of realistic shadows, angle of lights, reflections, and perspectives. Piero della Francesca (c.1415-1492), an early Renaissance artist, was also a mathematician and authored many books on perspective and geometry. Graphic artist M.C. Escher (1898—1972) was known for his mathematically inspired work; he used polygons or shapes such as squares, and triangles to create his art.

In conjunction with the artists’ use of mathematics in art, mathematicians have developed mathematical functions that can result in fascinating and complex patterns and shapes.

One example is Fractal art. Fractals represent objects with self-similarity; each shape is made of smaller copies of itself. Fractals are seen in nature in many instances such as trees, roots of trees, the human heart, lungs, kidney, vegetables, mountains, sand dunes, granite patterns, and many more. Have you ever looked down from the window on a plane and noticed the pattern of rivers? This is an example of fractals in nature; small rivers combine to form the larger river. Cauliflower is another interesting example of Fractals seen in nature.  If you look at the shape of a cauliflower, then cut it into pieces, each small piece looks like the larger piece but it’s smaller.


photo 2

Photo by Azi Sharif



Fractals in the world of mathematics are beautiful complex images that can be produced by iterating simple equations. One of the most well known examples of Fractals is the Mandelbrot set invented by Benoit Mandelbrot. It shows how iteration of a simple equation can result in amazing shapes with such complications, harmony and beauty.


                                               Mandelbrot set applet 

And more fascinating images created by Math!

photo 6

Wolfram Demonstration Projects, Flower Fractals

photo 5

Wolfram Demonstration Projects, Generating Patterns Similar to Peruvian Textiles



1 2 3