NASA Black Hole Visualisation

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I was expecting to see the background light being blueshifted enough to be visibly changing color. Is the effect just not visible in the simulation or is my expectation wrong? In the case of crossing the event horizon the caption mentions a blueshift in excess of 43 but how is that visible? Perhaps they left out the effect to allow people get a visual feedback on how the "geometry" of the background sky is warped?
 
Filip Larsen said:
Is the effect just not visible in the simulation or is my expectation wrong?
Anyone?