• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
Terrell rotation or Terrell effect is the name of a mathematical and physical effect.
IMO Terrell rotation is neither a mathematical nor a physical effect. IMO it is sollely an observation effect. See also Reflection 1 - Terrell rotation
Terrell rotation is the distortion that a passing object would appear to undergo, according to the special theory of relativity if it were travelling a significant fraction of the speed of light.
IMO Terrell rotation has also nothing to do with Special Relativity See also Reflection 2 - Special Relativity

### 1. Further detail

Terrell's and Penrose's papers pointed out that although special relativity appeared to describe an "observed contraction" in moving objects, these interpreted "observations" were not to be confused with the theory's literal predictions for the visible appearance of a moving object.
This whole sentence is confusing.
Thanks to the differential timelag effects in signals reaching the observer from the object's different parts, a receding object would appear contracted, an approaching object would appear elongated (even under special relativity) and the geometry of a passing object would appear skewed, as if rotated.
This sentence is correct with two remarks.
1. I would not mention: even under special relativity.
2. The geometry of the object when it passes the observer is distorted.
A previously-popular description of special relativity's predictions, in which an observer sees a passing object to be contracted (for instance, from a sphere to a flattened ellipsoid), was wrong
It is important to make a clear distinction between the Terrell Rotation and Special Relativity. Terrell Rotation has to do what one observer sees (observes). No physical changes are involved.
Special Relativity has to do with performing measurements (independent of human activities). Physical changes could be involved.

### Reflection 1 - Terrell rotation

Terrell rotation is strictly an observational effect.
Terrell rotation (my understanding) comes in two flavours: Length contraction and Length expansion.
• Length contraction related to Terrell effect is the observational effect that the length of an object, which moves away from an observer (while in movement) appears even shorter than stictly based on distance.
• Length expansion related to Terrell effect is the observational effect that the length of an object, which moves towards an observer (while in movement) appears longer than stictly based on distance.
The explanation is as follows:
• For an object, which moves away from an observer (while in movement) it takes more time to see the front of the object than the back. That means you will observe the front at an earlier moment, which implies that the length observed is shorter than strictly based on distance.
• For an object, which moves towards an observer (while in movement) it takes more time to see the back of the object than the front. That means you will observe the back at an earlier moment, which implies that the length observed is longer than strictly based on distance.

For a demonstration of this effect using Visual Basic see the following link: VB Train operation

### Reflection 2 - Special Relativity

It is my understanding that the Terrell rotation has nothing to do with Special Relativity and as such is no demonstration of SR. The length of the moving object is considered fixed.
That does not mean that SR could not be involved and that the length could vary as described by SR. But that is not considered.