Does repeating one word to form a password result in a similar pattern in its encrypted format?

Against a bruteforce attack the latter would be more secure, but the overall length of your password would already be hard to guess.

If someone however would know that you always repeat a regular word with a fixed amount of times, then a dictionary attack might be easier performed with the first example. (providing the person doesn't know about your signs)

With modern encryption techniques (1 way hashing and CBC) there isn't an easy way to notice repeated words.

Here's a place you can try it out with a bunch of different algorithms: http://www.crypo.com/tools/index.php

But the answer is no you will not see any repeating pattern. You may see that with xor encryption but you will never see that with a strong encryption algorithm. Password padding and repetition can be very secure unless someone knows that is what you do. To counter that all you have to do is throw in one or two extra characters to break the pattern and make it strong.

For example: securesecuresecuresecure.securesecure.

If you are unlucky, then a repeated password can result in a repeated encrypted text, it depends on the encryption that was used.

I never heard of patterns in a hash algorithm, so if a website only stores the hash (what it should), then you propably won't get such repeating patterns.

Should a website store the encrypted password, it can happen that you will see repeating patterns, if the ECB mode was used. That's why one should not use ECB anymore, instead use CBC or another mode. Here you will find a better explanation about EBC and CBC with good examples.