Is a design pattern considered a patent?
No. A patent is a legal limited monopoly on a specific invention. A design pattern is a documented general approach to solving a common type of problem. They're two completely different things.
No.
Design Pattern: a general reusable solution to a commonly occurring problem in software design
Patent: an official right to be the only person or company allowed to make or sell a new product for a certain period of time
The question makes no sense. A patent is something you have to apply and pay for, and which is then granted by a patent office.
So a valid question is "could a design pattern be patented?" And the answer is: probably not. The patent offices in different countries have different standards on what can and cannot be patented, but the general gist is that you can only patent practical applications, not abstract ideas. So a design pattern would most likely not be patentable.
You potentially could try to patent a new design pattern, but I doubt it would be very successful depending on the pattern in question. There is so much documentation and so many books regarding patterns currently in existence, that you would definitely run afoul of the "novelty" rule and the "prior art" rules to patent exclusion.
Hell, if Microsoft can try to patent the Visual Basic IsNot operator, then someone could try to patent a design pattern.
I think the answer is a definite NO. Since design patterns are, by definition, not specifically invented, but rather observed and recognized in already existing real world applications, "prior art" (an obstactle to patentability) will always apply.
I don't believe a design pattern could be patented, due to it necessarily being in common use in development (a pattern).
An algorithm on the other hand, is definitely patentable.