# Nikolay Shenkov

Summer School

Class of 2012

## Bio

I am from Velingrad, Bulgaria, a beautiful town in the heart of the Rhodopi mountains. I am a senior undergraduate studying physics at the University of Richmond, Virginia and I am interested in biological physics and systems biology. Particularly intriguing for me are the various computational approaches to understand biological complexity and how they can be integrated with the new experimental tools that are able to perform thousands of quantitative measurements in a single procedure. I hope to work toward connecting NKS computer experiments with theoretical predictions and lab results in biology. Outside work and study, I enjoy hiking and exploring cities by doing lots of walking.

## Project: Creating a Model for Growth with a Line and a Breaking Point

My project involves the creation and study of a simple model of biological growth in which a point on a line is chosen (breaking point), and then one end of the line is rotated by a fixed angle around that point. Once this is done, the breaking point can move to a different location, and the same cycle occurs. The decisions made at the breaking point can be modeled locally by a 3-color mobile cellular automaton where each color corresponds to rotation of the line upwards, rotation downwards, or no rotation at all. The breaking point can then move to the left or to the right on the line, which corresponds to the movement of the head of the mobile automaton. This constrains the breaking point to move a maximum of 1 unit of length for each cycle. As I progress through the project I may decide that another simple program is a better emulation for this behavior.

A key point in this project is the global constraint that the curved line is not allowed to intersect itself. This determines whether the growth was successful or has failed. Another element of the model we can include is line elongation after each cycle, which will add significant complexity, since now the automaton will need to make several more decisions.

I will start the experiment in two dimensions, but Carlo suggested that we should investigate the changes of the systems at higher dimensions as well. As we add more space for the line to develop in, the probability for the line to intersect will be decreasing, and we can study how the properties of each evolution change in higher dimensions. I am also interested in how successful evolutions (those that have satisfied the constraint) react to perturbations of the initial conditions. I can use this as a filter where I pick to study systems that are robust to changes in the initial conditions and observe how this robustness changes as we systematically change (mutate) the rules of the governing automaton.

Overall, there are many paths which the project can take (much like the line itself), and as I progress I will choose based on what is feasible and curious to examine from an applied NKS point of view.

## Favorite Four-Color, Four State Turing Machine

Rule 48530289241593464683167

• 22nd Annual Wolfram Summer School
• Bentley University, Waltham, MA, USA
• June 23–July 11, 2024