A Slower Speed of Light is a video game created by the MIT Game Lab which allows users to experience what it would be like if the speed of light was closer to normal walking/running speeds and thus experience relativistic effects in an otherwise familiar environment. From the site:
A Slower Speed of Light is a first-person game prototype in which players navigate a 3D space while picking up orbs that reduce the speed of light ... [allowing] the speed of light in the game to approach the player’s own maximum walking speed. Visual effects of special relativity gradually become apparent to the player [as more orbs are collected]... These effects, rendered in realtime to vertex accuracy, include the Doppler effect (red- and blue-shifting of visible light, and the shifting of infrared and ultraviolet light into the visible spectrum); the searchlight effect (increased brightness in the direction of travel); time dilation (differences in the perceived passage of time from the player and the outside world); Lorentz transformation (warping of space at near-light speeds); and the runtime effect (the ability to see objects as they were in the past, due to the travel time of light).
When I play the game and collect enough orbs for relativistic effects to really start becoming significant something happens that I didn't expect: as I accelerated towards objects they appeared to move further away from me (despite length contraction definitely being taken into effect, since I was able to get to those objects faster over a given distance than had I not collected any orbs). Luboš Motl in this question says that this is due to:
the shrinking of transverse directions if you're moving forward (or their expansion if you move backwards) which makes object look "further" (optically smaller) if you're moving forward. Because of this shrinking, you may effectively see "behind your head". You also see things how they looked like some time ago.
Based on my understanding of the Lorentz transformations the directions transverse to one's motion aren't effected ($y'=y$ and $z'=z$ if all motion is in the $x$ direction). So, what exactly causes this effect that I see in the game and Luboš Motl explains? Am I misunderstanding the Lorentz transformations?
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