Dropping a rock

This is a an illustrative demonstration of from the puzzle. I did this with little time. Options such as animating the rock, illustrating the effect of different densities of rock or object, e.g. floating objects and changing to assess and quantify the change are all options (a low priority on a CDF todo list).

Local maxima in permutations

This post accompanies How many bumps?.

The CDF is the graphical illustration of the permutations of numbers to 1 to n (in this case illustrating 2,3,...,6). The average is calculated using a function that counts the local maxima in each permutation and then averages across all permutations. This quickly becomes unwieldy. The simplicity of the solution and the efficiency and beauty of the derivation provided by Professor Blitzstein is now self-evident.

It would have been nice to color the local maxima: perhaps another post.

Network flow

This is a interactive illustration of a simple graph. The source is the left most node and the sink the right most node. The edge capacities are frame and blue The flows are frame with red text and yellow backgrounds. The subgraph highlighted in red illustrates the maximal flow.

The sliders change the capacities on the graph.

Hidden in plain sight

This may have been a relatively easy detection exercise but using Mathematica allowed visualization.