The self-similar (fractal) cluster obtained using diffusion-limited aggregation on a square lattice. The growth of the cluster is shown with time with the motive to show the increment in the number of screened particles (significant screening effect) with an increase in time.
Ever since I came across this simple algorithm, famously known as ‘diffusion limited aggregation’, my fascination for it has grown even more with time. In an environment where diffusion is limited, the algorithm lay down the simple steps for the growth of clusters that are self-similar and are known as fractals. The reason for it to be so famous is the extraordinary similarity between the structures obtained via this algorithm to naturally occurring objects like leaves on a tree, mineral oils in rocks, diffusion of smoke in air, tissue engineering, etc. Scientists of nearly every scientific discipline have used it to mimic growth and inspect its scaling behavior. This surprising similarity compels me to perceive that, perhaps, growth of everything on earth has something universally common. While pondering over these aspects in one of my train journeys home, something prompted me to start relating the details of the algorithm with the socioeconomic growth of our society.
‘Diffusion limited aggregation’ depicts a random process wherein a particle is placed at the center, acting as a nucleation point. Other particles move randomly, unknown to the particle at the center. Once the randomly moving particles come near to the nucleation point, the particles attach to it and the particle at the center starts growing into a cluster. At the end of the process, all the particles are stuck to the growing cluster.
Indeed, in the starting phase of the cluster growth, every particle at the periphery of the growing cluster has equal probability to grow. But, as time increases, there builds an intermediate situation where some of the particles are screened from the randomly moving particles. This results in lower growth probability for screened particles and higher growth probability for unscreened particles. The “screening effect” can be clearly observed in the starting phase of its emergence.
However, with increasing time, a saturation phase is reached where the screening becomes more prominent and there is little scope to change anything. Depicting that it is too late to reverse the effect of screening which could have been controlled with proper measures, if taken earlier.
Relating this to the socioeconomic growth of our society, the particle at the center represents a person waiting for an opportunity to grow. The randomly moving particles depict the resources needed for the growth of the person. A person in a society always needs some resources for his/her growth and resources are always around us moving in a random way, unless we approach them in a systematic and planned manner and can use the resource for his/her growth.
However, the case where every person is equally probable to receive the resources is a luxury of a small group of people in our society. In most of the cases, a larger section of the society is deprived of the opportunities that are being promised. As if they are screened from the resources and thus cannot grow as smoothly as those who can easily acquire those resources.
In the algorithm, the visualization of this screening effect is so apparent, but is the most difficult concept to incorporate in a theory. Similarly, despite its prevalence, the rules which lead to the deprivation of resources from common people are hard to state in our society. It seems that the “screening effect” has become so obvious in our society that it is now a part of everyone’s consciousness.
I really wish that we have not reached a saturation phase where it does not matter even if we desire to change the course of the prevailing notion in our society; and we can still opt to demolish the “screening effect” from our society so that everyone has equal probability to grow and nourish themselves for a better tomorrow.
Anurag Singh is senior research fellow at Physics Department, IIT Kharagpur (WB) email@example.com