The Random class is designed to be a low overhead source of pseudo-random numbers. But the consequence of the “low overhead” implementation is that the number stream has properties that are a long way off perfect … from a statistical perspective. You have encountered one of the imperfections. Random is documented as being a Linear Congruential generator, and the properties of such generators are well known.
There are a variety of ways of dealing with this. For example, if you are careful you can hide some of the most obvious “poor” characteristics. (But you would be advised to run some statistical tests. You can’t see non-randomness in the noise added to your second image, but it could still be there.)
Alternatively, if you want pseudo-random numbers that have guaranteed good statistical properties, then you should be using SecureRandom instead of Random. It has significantly higher overheads, but you can be assured that many “smart people” will have spent a lot of time on the design, testing and analysis of the algorithms.
Finally, it is relatively simple to create a subclass of Random that uses an alternative algorithm for generating the numbers; see link. The problem is that you have to select (or design) and implement an appropriate algorithm.
Calling this an “issue” is debatable. It is a well known and understood property of LCGs, and use of LCGs was a concious engineering choice. People want low overhead PRNGs, but low overhead PRNGs have poor properties. TANSTAAFL.
Certainly, this is not something that Oracle would contemplate changing in Random. Indeed, the reasons for not changing are stated clearly in the javadoc for the Random class.
“In order to guarantee this property, particular algorithms are specified for the class
Random. Java implementations must use all the algorithms shown here for the classRandom, for the sake of absolute portability of Java code.”