A simple toy parton shower shown at the "PSI Summer School Exothiggs", Zuoz, August 2016 (https://www.psi.ch/particle-zuoz-school/ltp-zuoz-summer-school), as part of the "Ingredients for accurate collider physics lectures" by Gavin Salam.
This is not meant to be a realistic shower, but rather a very basic illustration of how the core of a shower works.
The shower generates the transverse momenta of all primary emissions for a colour-singlet system (e.g. Higgs) that is produced by gluon fusion
Many important physical effects are missing:
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energy conservation and the effect of PDFs, because the shower works in the soft approximation
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secondary emissions, i.e. the radiated gluons don't themselves radiate here
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running coupling
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generation of actual 4-momenta for the emissions (only the transverse momenta are generated)
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etc.