What do buttons, dartboards, a Black Forest cake and the Colosseum have in common?


Exactly, they are round. More precisely, circular. Or even better: If you measure their circumference and divide it by their diameter, you always get one number: π, pi.


Pi (π) is one of those famous constant numbers that keep popping up in all sorts of different fields. Many calculations, many formulas, and most things that feature a circle ultimately depend on its 3.141592…. Even those who are searching for Nessie bump into .

Finding Nessie

Imagine a person trying to take the best photo of Nessie, the Loch Ness monster. Hundreds of people have tried it. The lake itself is quite large (a surface of 56 km2). So, not an easy task. Where would you start looking for Nessie? The best technique: where it was last seen. At least you know that Nessie once stayed  in that part of the lake. 


World Pi Day at Complexity Science Hub


The issue is that the monster moves, and even if it moves slowly, the area that we have to search grows pretty quickly. For example, if Nessie moves at a speed of 1 km per hour, what is the area we need to search? Just one hour after the last known report, the monster could be anywhere within a circle with an area of 3.14 km2. And in two hours, the area will be 12.6 km2. So the area where the monster is sure to be after h hours since its last sighting is πh2.

Pi (π) in cities and people

Let’s leave Nessie alone again, nevertheless appears almost everywhere. Besides circles and countless mathematical formulas, you can find it playing pool. Even in the Bible. As well as in cities. And it works like this:


If you randomly distribute points in a circle with radius r, you you may be (more or less) stunned (depending on whether you are stunned by at all) to find the following: The average distance between points is 128r/45. The same formula is used over and over to model various aspects of urban transportation and traffic flow. For more than 40 years, we have been modeling cities using the same formula.

Commuting by pi

If you know the area of a city, say A, then traveling from one location to another will grow according to 128√A/45π. This formula holds for cities that are perfectly circular (perhaps a very simple city!) and where you can travel in a straight line between any two points. Of course, no city is like this, but it gives us an idea of how long trips will be and how long the commute will take.


Vienna, for example, has an area of roughly 415 km2. So if we take any two locations in the city, they are on average 18 km apart. However, Innsbruck has a surface of 105km2, so on average the places are 9 km apart. This is shown in a recent study by Rafael Prieto-Curiel of the Complexity Science Hub, who, together with colleagues, measured about 183 million buildings in African cities. He used a similar formula to the one for the distance between points inside a circle can also be used to measure distances between buildings in a city.

World Pi Day at Complexity Science Hub

There are other aspects of cities, including their irregular shapes, the space between its buildings, the many roads or its fractal patterns. However, keeps appearing! 


Last but not least, does not even stop at the city boundaries. Instead, the fascination with lives in the heads of people. This culminates in worldwide competitions  in which people try to outdo each other in enumerating more digits of . The official world record is currently 70,030 digits. It took Suresh Kumar Sharma 17 hours and 14 minutes.


This was in 2015, and no one has officially beaten it since. But developer Emma Haruka Iwao announced another record on June 8, 2022: a program from Google calculated the circular number to 100 trillion digits. That took 157 days. By way of comparison, in 1940 scientists were only able to calculate around 1,000 decimal places.


Happy day! A day for mathematicians, people who like math, or even people who suffered from in school but can still remember the first digits of 3.14!

Liuhuaying Yang, the data visualization expert at the Complexity Science Hub, wins first place of the World Dataviz Prize 2023 in the interactive category.


Her work Four Seasons: How Has the World Progressed in Recent Years “uses the metaphor of a tree in different seasons to spotlight different aspects of progress.”

The prize is awarded by Information is Beautiful and the World Government Summit, which provided the datasets and concepts. This year, the competition focused on the past, present, and future of society and governments. Hundreds of designers and developers from all over the world created data-visualizations that tell a story about the data.

Beautiful and elegant

Yang’s “beautiful and elegant visualisation” illustrates how the world has progressed in recent years. Each season emphasizes a different aspect of development. Spring is a time of growth; summer represents prosperity; fall is a time of change; and winter is the season for preparing for crisis. 



Additionally, each tree illustrates how the world stands in the present (branches), the past (roots), and the future (sky). “The roots show global performances over the past 10 years, as the past provides foundation for the present and future just like roots of a tree,” explains Yang. “The sky visualizes the buzz of 20 development and 18 innovation frontiers from seven categories. And development and innovation are like the sunlight and rain that provide energy and water for a tree to grow and flourish.”


“I always find it fascinating to have a metaphor in data visualizations. And a tree is easy to start with, because it can work well with hierarchy dataset,” points out Yang. 


“I also recalled the conversations with Fariba Karimi and Samuel Martin-Gutierrez about the illustration for presenting the first-mover advantage on gender disparities, where we tried to explain things based on tree, root, and sunlight, and this idea was originally from Dániel Kondor,” recalls Yang.

CSH/Liuhuaying Yang
Physicist Fariba Karimi and her team at the Complexity Science Hub Vienna revisited and analyzed the claims made by a ‘sexist’ senior scientist – who said, among other things, that women were less able at physics than men.

“A good visualization narrates a story. When I was experimenting with the tree idea for this project, I wasn’t satisfied with the narratives or the stories in the work. But while shopping for a jigsaw puzzle, I saw many versions of ‘four seasons’, and that was my ‘Aha’ moment.”


The works were judged by a panel of creative and industry leaders led by David McCandless from Information is Beautiful: Alberto Cairo a journalist, designer, and scholar who teaches visualization at the University of Miami; Amanda Makulec a data visualization designer and executive director of The Data Visualisation Society; and Gurman Bhatia an award-winning data journalist based in New Delhi, India. 

Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8
Vernissage ART&SCIENCE at Complexity Science Hub 23-01-27_8

Child pornography is sold and traded via relevant platforms on the dark web. Payments are made through cryptocurrencies, usually Bitcoin. Currently, the number of cases is exploding. And current events clearly show how necessary it is to be able to track the payment flows in the trade of child pornography material.


The technology to do so is ready. Data scientist and crypto expert Bernhard Haslhofer from the Complexity Science Hub is working with his team to develop methods that make just that possible. Researchers are using these methods to analyze the enormous flood of data and thus unveil the financial flows in the context of child pornography. This allows them to uncover connections between child pornography platforms. Automated tracking of payment flows tracks down consumers who purchase such material on the one hand, and the operators of such platforms themselves on the other.


These network analyses can support investigations by the authorities. Partnerships with Bavarian authorities are already showing initial success. Network analysis helps structuring the increasing number of cases, enables targeted action and enhances efficiency. “We live in the age of digitalization. Tomorrow will look different from today. This also affects cybercrime and child abuse in particular. For this reason, it is important that we think about methods today which we can also use tomorrow. Personally, I am pleased to be able to make a contribution here,” says Haslhofer.


Stefan Thurner, President of the Complexity Science Hub, also emphasizes: “Research in the digitalized world like this, where the analysis of huge amounts of data results in immediate benefits for the population – that is what we are committed to.”


For inquiries, please contact our press office:
Anja Böck, boeck@csh.ac.at, +43 1 59991 601


Further information and details on the first results of the cooperation with the ZCB will be presented at the press meeting at the Complexity Science Hub on January 31.

What if Belgium stopped producing beer? Discover how the world’s supply chains are interconnected and interdependent. Check out the Complexity Science Hub’s 𝗙𝗼𝗼𝗱 𝗦𝘂𝗽𝗽𝗹𝘆 𝗦𝗵𝗼𝗰𝗸 𝗘𝘅𝗽𝗹𝗼𝗿𝗲𝗿 and create your own scenarios.

Food Supply Shock Explorer © Complexity Science Hub

The war in Ukraine called attention to the vulnerability of the global food supply system. With the Food Supply Shock Explorer, you can explore which food products are lost and which countries are affected most severely when a specific supplier stops to produce a single food product. Key scenarios related to Ukraine and a detailed description of our model are presented here: https://doi.org/10.48550/arXiv.2210.01846.


The model combines information on the trade, production, and consumption of 125 food products in 192 countries. As products turn into other products along the supply chain, the shock to Ukrainian maize production does not only affect the availability of maize but also causes losses of other products, such as pig or poultry meat due to a lack of animal feed.



For more information on supply chain research at the Complexity Science Hub, click here.


On Nov 29, Complexity Science Hub Vienna (CSH) invited international experts to discuss the resilience of supply chains. The researchers were united in their Christmas wish: more data.


Public Panel at CSH about Supply Chain Resilience
Public panel discussion at CSH on supply chain resilience


We are currently facing multiple crises: Inflation crisis, energy crisis, democracy crisis, migration crisis, political crisis, information crisis, not to mention the Ukraine crisis and the climate crisis. “The next possible crisis we should be prepared for is that of supply chains. We have already seen the first signs that a supply crisis is possible,” Stefan Thurner from Complexity Science Hub states.


Small disruptions can grow big


Supply chains can grow to thousands and thousands of firms, where small disruptions are able to cascade across global networks. Therefore, it is crucial to increase their resilience. “To really understand supply chain resilience, we need to understand economics,” explains Doyne Farmer, of the University of Oxford and External Faculty at CSH.


Avoiding energy bills from skyrocketing


For this reason, it is essential to get data. This is immensely relevant right now, since a very concrete, current example shows us the importance of making supply chains more resilient: at the moment, people’s energy bills are suddenly skyrocketing due to problems in the supply chain, Farmer says. Bottlenecks like these could be avoided in the future.

Furthermore, if we had been able to predict how the pandemic would affect supply chains, we could have started producing masks sooner, according to Farmer. Data-driven, interdisciplinary models create entirely new opportunities in this process.


New picture of the world


“Now, for the first time, we are seeing supply chains at firm level, and that opens up a total new picture of the world,” Thurner states. This research approach is still at an early stage, but at a CSH workshop this week alone, international researchers presented several new methods that allow us to identify the weak spots of the economy and ensure that supply chains will remain intact, Farmer says.


Christmas wish: more data


For the future, the scientists would like to see one thing above all: more data and more transparency. „Visibility can now be increased through means that were previously not possible. The use of predictive tools, or AI algorithms, has made digital supply chain surveillance possible on a scale that was not previously possible,” Alexandra Brintrup, of the University of Cambridge says.

The data needed to do that has to be very accurate, whereby details matter a lot. Besides, new methodologies, like using phone data, government and tax data play a crucial role. “Science will depend on the ability of governments to get the data and host it in a secure way,” Thurner says.


Getting this idea into people’s heads


Karin Doppelbauer, Member of the National Council, puts this in a governmental perspective: “I don’t even think there is a vision from governmental perspective on how to manage the data so that it is used transparently and the security of the data is maintained. Additionally I think the third question is what we want to do with the data.” Governments sometimes look at these new technologies in a way that is more about what they can restrict, rather than seeing the opportunities, she continues. “First of all, we have to think about how we can get this issue into the hearts and minds of the people,” because, at the moment, Doppelbauer does not see that happening in Austria. “We should paint a picture that shows the possibilities,” she said.


Challenge for industry


Companies , moreover, face another conflict, namely whether data on supply chains should be public or not. “The answer is yes and no. Resilience in supply chains is a competitive advantage. It is important [for companies] to protect its competitive advantage and resilience and not let anyone see them. The flipside – as we saw during the pandemic – is that we can only understand what is coming down the line if we collaborate to have resilience in multiple supply chains,” Byron McGill from Aviva Insurance states.

In any case, there is agreement on one thing: in the future, the resilience of supply chains will play an important role – in politics, business and science.

Population has not only grown


WORKSHOPSince humans discovered agriculture, population has grown rapidly. However, repeated declines also occurred, even among the first farming communities. International experts even among the first farming communities. International experts explored  a wide range of evidence  for this along with several possible explanations in a CSH workshop.



It is well known that over the past 10,000 years, since people started to settle and doing agriculture, human population has grown tremendously. Yet, more and more evidence is accumulating that this growth was not monotonic, but interspersed by periods of declines, often associated with severe crises.

„One very dramatic example of true population collapse affected the Cucuteni-Tripolye-Culture in the 4th millennium BCE. At its peak, there were large proto-cities with 10,000 or more inhabitants, but after a complete depopulation of the area archaeologists could not find any evidence of habitation for 600 years following the collapse,” CSH-Researcher Peter Turchin explains.



It happened also in the Neolithic


What is the Neolithic period?

Humans have adopted agriculture and settled lifestyle, but not yet the use of metals to any significant extent.

Date ranges of it vary based on the region considered – starting around 10,000 BCE at the earliest and lasting typically until 4,000-2,000 BCE in Eurasia.

Well-known cases over the course of written history has been studied extensively. Less attention has been paid so far to population declines during the Neolithic, a period without large-scale political organization, writing or use of metals. Yet, population busts following booms seem to be an important feature of this period as well. So far, there is no consensus on the cause (or causes) of such declines, even though we know that Neolithic people faced many challenges.



Manifold possible drivers


In this workshop, hosted by Complexity Researchers Peter Turchin and Dániel Kondor, experts with a wide range of knowledge on Neolithic population history joined us at CSH Vienna to accumulate their knowledge about estimates of population growth or decline. „We now understand that population declines are a common phenomenon, although there are differences in how this happened and factors that might have been important,“ Kondor says. Possible drivers of population trajectories include the variety of challenges faced by early farmers like changes in climate, overexploitation of resources, conflicts, warfare and diseases.



Dániel Kondor and Peter Turchin at CSH Vienna



Regions of special interest


„We discussed knowledge on the population history of several world regions, concentrating on evidence of alternating periods of population growth and decline, so-called booms and busts,” Kondor explains.


The Central European Neolithic is one of the cases with a lot of research. Farmers, arriving from Anatolia across the Balkans, settled the region from present-day Hungary to the Netherlands in the 6th millennium BCE. They were quickly growing in numbers, which indicates that they apparently managed to be well adapted to the local conditions. Significant population decline happened 300-500 years after initial settlement, with some regions abandoned almost completely. Besides Europe, other important regions of Neolithic settlement, for example in China, are also in the focus of research.


Fascination of collapse


“Everybody is fascinated with the collapse of large-scale complex societies. Many thinkers have proposed that “collapse” – as manifested by a drastic decline of the society’s size or a so-called a population „bust“ – is the price we pay for social complexity. But as our knowledge of population dynamics of “simple”, small-scale societies of Neolithic farmers became more detailed, thanks to intense archaeological research, we learned that these societies were, perhaps, even more susceptible to population busts than later states and empires. The causes of such busts remain mysterious. There are many hypotheses but no scientific consensus so far”, Turchin says.



Participants in-person:


Stephen Shennan (UCL)

Johanna Hilpert (Christian-Albrechts-Universität zu Kiel)

Detlef Gronenborn (RGZM)

Ruiliang Liu (British Museum)

Zhiwu Chen (HKU)



Participants online:


Alessio Palmisano (Universitá di Torino)

Martin J Smith (Bournemouth University)

Aleksandr Diachenko (National Academy of Sciences of Ukraine)



International workshop participants at CSH Vienna

Frank Schweitzer marks the 25th anniversary of the journal ACS with the book Agents, Networks, Evolution


In celebration of the 25th anniversary of the journal Advances in Complex Systems (ACS), Frank Schweitzer’s new book gives an overview of some of the most relevant developments in complex systems science over the past two decades.


It would not have been possible for complexity science to succeed over the past 25 years without pioneering institutions such as the ACS, claim CSH president Stefan Thurner and University of Chicago professor Luis Bettencourt in the book’s preface. “These pioneering venues provided the fora for communication, coordination, selection of ideas and cooperation between scientists. ACS, as one of the traditionally relevant journals in the field, covered the history and the remarkable transformation of complexity science over time. This is also reflected in the present book,” point out Thurner and Bettencourt.


The book, divided in four chapters, covers four different modelling approaches in detail: agent-based models; networks; system dynamics; and evolutionary dynamics. In each chapter, Schweitzer, a CSH external faculty member and professor at ETH Zurich, summarizes the essential concepts and discusses the main research directions and applications in various fields. Additionally, each chapter presents reprinted publications relevant to modeling complex systems from different disciplines.


Communicating to non-experts


These insightful introductions, written by Schweitzer, the editor in chief and the driving force behind ACS for many years, make the book more accessible to non-experts, according to Thurner and Bettancourt. The intelligible and enjoyable texts “should help to spread recent developments in complexity science to a younger audience and scientists outside the field.”


Agents, Networks, Evolution – a Quarter Century of Advances of Complex Systems, published by World Scientific Publishing Co., is freely available as PDF. You can download your copy here: https://www.worldscientific.com/doi/epdf/10.1142/13184


38 students, two weeks in Vienna and a lot of complexity science


Yippiiiiiiiie! After (almost) years of intensive preparations, it finally started today: the first Complexity GAINs International Summer School!


The program is a collaboration of the Santa Fe Institute (SFI) with four leading complex systems research institutions in the EU, namely



(The “GAINs” in the program’s title is formed by the initials of the participating countries.)


In a competitive application process, 18 PhD students from the US with backgrounds in the physical, natural and social sciences, and mathematics as well as 18 PhDs from the partnering EU institutions were selected to spend two weeks in Vienna to receive the latest insights into complexity science.


A great opportunity to learn about complex systems


Complex systems, from a cell to the planet, exhibit adaptive responses and thus demand innovative approaches to uncover their emergent properties and dynamics. It requires not less than methods that exceed traditional academic fields.


Although such a broad understanding is highly needed to address all kinds of challenges humanity is facing – from ecological sustainability to disease dynamics, from collective and artificial intelligence to belief propagation or financial risk –, only a few training programs exist to provide that knowledge.


The Complexity GAINs Summer School was created to fill that gap. It will provide PhD students with the theory and methods to model and understand complex systems. They will gain foundational knowledge and practice in modeling complex systems of interest using approaches from physics, computer science, biology, social sciences, and mathematics.


The prestigous program will run over three years. Each year will focus on different systems.


In 2022, we start with social-behavioral systems, in particular: “Disintegration of societies: Quantitative modeling of complex socio-behavioral systems.”


2023 and 2024 will focus on intelligent systems, and ecosystems, respectively.


More to come – stay tuned!

First Complexity GAINs Summer School opening in TU The Sky.

The Vienna–Lviv connection


When you visit the Hub these days, you certainly will see our guest from Ukraine sit in the shade of a tree, a laptop on his knees, working.


Yurij — as friends we can call him Yurko — Holovatch is professor in physics at the Institute of Condensed Matter Physics of the National Academy of Sciences of Ukraine. He arrived in Vienna about a month ago and will alltogether spend two months as a CSH Visitor with us before heading back to Lviv.


Yesterday, Yurij gave a talk about magnetic phase transition and complex systems. “It’s often said that complex systems science gains insights from physics. But there is knowledge from complexity science that is implemented to study physical phenomena too. In my talk, I tried to show that this is a mutual exchange,” he explained. 


His passion for connecting with people goes beyond sharing his knowledge. Whenever he speaks about his conversations with some of our young scientists – or any other people, as it is -, he is enthusiastic and positive — just the most friendly and kindest person. “I have met such interesting and intelligent people, and it has been such a great experience to learn what they have been studying,” he said.

In the future, Yurko envisions new collaborations and partnerships with CSH scientists. “I can see working together with the Hub on three different topics: transportation networks, migration of Ukrainians, and mythology,” he said.


We are looking forward to it!

Yurij Holovatch (in the foreground) was a participant of Diego Rybski's workshop "Cities as Complex Systems"