I am behind in creating a video for the TailBub, however, let me try to see if I can explain it briefly here.
The following is an aether that contains 3 ways of creating the same function. The function we are creating is a function that will calculate the smallest factor of a number (as was done in the Recursive Mech
Each of these methods (SF, ISF and TSF) use an external Mech to "wrap" the internal calculation. This is done so that we can seed the starting test number with a 2. The SF / iSF calculation is the same as the MechBubs created in the original recursive mech video (except for a minor bug fix).
The ISF / iISF version makes use of the new IfBub in order to accomplish the same thing. This version has two advantages over the original calculation. First, the IfBub is more visual, making the calculation more readable. Second, the IfBub only evaluates the appropriate resultant (either the 'then' or the 'else' not both), which prevents the automatic stack overflow problem. The original Mech solved this issue by using Function type values rather than numbers which added some complexity to the calculation.
The TSF / iTSF version replicates the same calculation again this time using the new TailBub. The new TailBub has a name and parameters section just as in the original MechBub, but also has a new looping structure, that consists of a 'while' section, an 'iteration' section and a new 'result' section.
The first section below the parameters is the 'while' section. The TailBub will iterate until the 'while' section evaluates to 0 (i.e., false). If the while section is true, than each of the parameters is modified as specified in the 'iteration' section. There will be one 'iteration' bubble for each parameter. Once the 'while' section is no longer true (i.e., evaluates to 0), then the result bubble will be evaluated using the parameters of the last iteration.