Irreligion: Fountain of chaos

By David Hale | July 19, 2025

David Hale. Courtesy photo

What would another warm summer be like in Aspen without little children joyfully running (and screaming) through Aspen's famous "Dancing Fountain." So here is today's quiz: What do those screaming little monsters have to do with tomorrow's weather?

This story begins with a local legend, Nick DeWolf, who passed away in 2006. DeWolf was born in 1928 and was educated at MIT, where he graduated in 1948 at the age of 19. In 1960, he co-founded Teradyne, a company that built the first computer operated integrated circuit tester. He was CEO of that company for 11 years. In 1971, he moved to Aspen with his wife, Maggie, and six kids. Somewhere around 1980, DeWolf and Travis Fulton (who helped start the Anderson Ranch Arts Center) were asked by the city of Aspen to build the famous "Dancing Fountain" on the Mall. I have a vague memory of an interview of DeWolf in the early '80s where he said his inspiration for the fountain's randomized computer program came from chaos theory.

Edward Lorenz stumbled upon his idea for chaos theory in 1961 while re-running a simple computer program he had designed for weather forecasting. At one point, he paused the program to take a break (It took hours to run). When he restarted it, he was surprised to find that it yielded a completely different forecast. He discovered that when he paused the program, it automatically rounded a number off. That single change created a completely different forecast. This became the basis for "perturbation theory" — certain systems have a hyper-sensitivity to their initial conditions. This theory was made famous by a 1972 paper Lorenz gave, entitled: "Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" This theory and the three non-linear equations that illustrate it became known as the Lorenz Attractor. When these equations were first graphed, they looked like butterfly wings. Coincidence? Lorenz would never say. More importantly, the graphed lines never repeated exactly. There was a pattern without an exact reiteration. Like leaves, snowflakes, and people, no two are exactly the same.

In 2009, all three of the fountain's backup computers that DeWolf had programmed crashed. So Aspen Parks and Recreation contacted Travis Fulton and Peter Hutter to see what could be done. They soon discovered DeWolf's equation for the fountain's operation was written in a dead code called Assembly Language. They searched far and wide and could find no one who could decipher the code. Months later, Fulton and Hutter were supervising a project that involved heavy equipment moving boulders around. They were talking about their problem finding anyone to break the mysterious code when the guy operating the front end loader hopped down and said, "I can read Assembly Language." His name was Rodger Hollingsworth Jr., and it didn't take long before he had rewritten the code in a modern computer language.

Aside from Aspen's famous fountain, chaos theory now underwrites modern weather forecasting. It can be seen most obviously in what's called "ensemble" forecasts. When you see those "spaghetti graphics" that forecast hurricane movement, those are based upon perturbations. If you go to the National Oceanic and Atmospheric Administration's NWS site for Aspen, under the Forecast Discussion you will usually see the word "ensembles" used. It will also appear as a link to "Ensemble Forecasting." Under that tab, there is the statement that these forecasts use "multiple predictions from an ensemble of models with slightly different initial conditions (think of a butterfly's wings) used as input and/or slightly different versions of models … averaging the various forecasts, which eliminates non-predictable components." The only thing wrong with this synopsis is it should say that these averages, "… attempt to eliminate non-predictable components." The qualifier is necessary because chaos is always working to undermine perfect predictability. The title of Lorenz' other famous paper "Deterministic non-periodic flow" also highlights my qualifier. Is aperiodicy (chaos) somehow determined (or governed) just because it has parameters? This is a question germane to fractal propagation, the step child of chaos theory.

Most people want security in their lives. Not just with weather, but work, health, finances, etc. What would a world of perfect predictability look like? How exciting is A = A or "a night in which all the cows are black"? We don't have to worry about a world of perfect predictability because chaos (difference) always lurks nearby.

Will DeWolf's fountain ever repeat? Fulton said it would take 75,000 iterations before it would repeat. Hollingsworth said it would take hundreds of thousands. I recall DeWolf himself saying it would never repeat.

Nick DeWolf was truly a visionary. He started so many community-based nonprofits. Here is a short list: GrassRoots Community Network, which brought cable TV to the Roaring Fork Valley, WE-cycle — Aspen's bike share program, Rofintug web hosting (now Rof.net), and the Aspen Center of Physics' Winter Lecture Series, to name a few.

Check out the fountain. And ask yourself, what is more chaotic? The "deterministic non-periodic flow" of the dancing water display? Or those delighted happy screaming little kids?

---

David Hale earned his Ph.D. in Philosophy, Religion and Cultural Theory from the University of Denver and Iliff School of Theology. He is a lecturer in Philosophy at Colorado Mesa University in Grand Junction and is a full time contractor in Snowmass.