If it was really glycerin, the areas would be runny or goopy, so to call it "glycerin rivers" is a bit of a misnomer. Some call it stearic streaking. Probably the most accurate name is just "streaking" or "mottling".
Soap is made of many different kinds of soap molecules. As the soap cools in the mold, some parts of the soap may harden before other areas do. That affects where the colorant ends up. Also some soaps are clear and others are opaque. This creates the streaks or mottles -- areas of clear soap surrounded by colored or opaque soap.
Any soap can streak, but slow cooling or gelling of the molded soap, the use of titanium dioxide colorant, and the use of palm oil that was not well mixed before use seem to increase the chance of streaking/mottling. Soap cool, don't gel, put your powdered colorants in glycerin, oil, or water and let them stand for several hours before use so they get thoroughly wetted, and mix palm oil well before measuring it.
I also suspect the way the soap is put into and manipulated in the mold is also a factor, since the streaks are often aligned with the way the soap has been spooned or poured in and/or swirled in the mold. You can see that in your soap -- the clear soap streaks are parallel to the color change. Not sure how to avoid this technique-related streaking.