Dendrites can form during solidification making ice or metal crystals

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

There is an xkxd comic by Randall Munroe on September 19, 2025 titled Phase changes. The accompanying Explain xkcd web page says the title text is:

 

“People looking for the gaps in our understanding where the meaning of consciousness or free will might hide often turn to quantum uncertainty or infinite cosmologies, as if we don’t have breathtakingly complex emergent phenomena right there in our freezers.”

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Those spikes are branching (often repeated) which is a feature of crystallization called dendrites. They can be seen in snowflakes, as is shown above. There are Wikipedia pages both for Dendrite (crystal) and Dendrite(metal). But both omit the much earlier 1963 and 1964 Mullins and Sekerka magazine articles describing the physics of morphological stability. An unstable solid-liquid interface leads to formation of dendrites. There is an article by Dmitri V. Alexandrov and Peter K. Galenko in the Journal of Applied Physics on August 1, 2024 titled The Mullins-Sekerka theory: 60 years of morphological stability.

 

Robert Sekerka is one the more interesting people I have ever known and taken courses from. When I was an undergrad at Carnegie-Mellon University, he described to a Metals Club meeting just how he got into metallurgy. His first job was as a metallurgy technician at Westinghouse Research Laboratories from 1955 to 1958. He worked for both William W. Mullins and William A. Tiller. Bill Mullins was later professor and head (1963 to 1966) of the Metallurgy Department at Carnegie Tech. And Bill Tiller was professor and head of the Department of Materials Science at Stanford (1966 to 1971).

 

Robert went to the University of Pittsburgh part time while working, and then got his B.S. in Physics in 1960. Then he went to graduate school on a fellowship and got a Ph.D. in Physics from Harvard University in 1965. While he was at Harvard, Sekerka coauthored those two highly mathematical articles with Mullins. He headed back to Westinghouse from 1965 to 1969 as a Senior Scientist. Then he moved to Carnegie Mellon University in 1969 as professor in Metallurgy and Materials Science. He was department head from 1976 to 1982. Later he was Professor of Physics and Mathematics and a Dean.