Hands-on option

Basic stage for the hands-on option

The height and the width of the tree as a whole are those of its root node. Determine systematically the how the width and the height of the resulting tree depend on the branching rate and the change factor in situations in which the maximum depth and the maximum total size are not reached.

Report in writing

• the design for the systematic exploration,
• the data you gather at each step of the exploration,
• the analysis of the gathered data, and
• the conclusions drawn based on the analysis.

Should you consult any sources in the process, remember to clearly cite them clearly.

In-depth stage for the hands-on option

Extend your analysis to the level of individual nodes and examine the degree distribution, again in situations in which the maximum depth and the maximum total size are not reached.

Is this a roughly symmetrical distribution? It is skewed left or right? Does it appear to be more or less normal? Is there a mathematical name for this particular distribution?

Note that you can add a console.log(n.degree); to the subroutine that draws the nodes to have these numbers appear in the web-developer tool console instead of writing them down yourself in case you wish to use a computational tool for the analysis.

Should you consult any sources in the process, remember to clearly cite them clearly.

Conceptual option

Basic stage for the conceptual option

Read about real-world branching processes and determine which ones "cool down" (change factors below one) and which ones do not (change factor roughly equal to one), and which ones "speed up" (change factors above one).

Try to find at least one example for each of the three scenarios, and if you find nothing documented, attempt to identify one by thinking about other possible branching processes yourself.

Remember to clearly cite any sources you may consult and share interesting information with fellow participants.

In-depth stage for the conceptual option

In our example branching system, new nodes are added but older nodes are never removed. A generalization of this model is called a birth-death process. In such a process, each node has a limited lifetime. Also, each node is born at a specific time and the speed of this happening may vary from branch to branch, creating a more blurry definition of "generations".

Read and think about the possible ways that lifetimes can be modelled by considering how and when births and deaths take place in diverse kinds of branching processes. Consider also non-organic processes: for example, electronic components or road pavements have a "useful life". Socioeconomic phenomena as well involves the rise and fall of elements (companies get founded, merge, split or cease operations).

Document your thoughts and findings in writing, clearly citing any sources you consulted in the process.