As an element of design rhythm and pattern are similar in the sense that both are a form of repetition. The difference between them is that rhythm encourages movement of the eye across the image whereas pattern is more static and is most effective when it fills the frame as the assumption is that it continues beyond the edges of the frame.
Rhythm suggests movement and activity and works best when there is a natural break in the elements, otherwise the picture may become predictable and boring.
Examples of Pattern
|Man made pattern|
|Pattern with the helping hand of mother nature.|
Example of Rhythm
As an example of rhythm this image has the "optical beat" suggested by Michael Freeman in his book "The Photographers Eye" and moves the viewer from the front of the image towards the back - however with this particular image the missing element is a focal point to maintain our interest. In order for rhythm to be effective in an image there needs to be an element that attracts and hold the viewer's attention otherwise, like the image above, the outcome is boring and predictable. Again as we tend to read from left to right the rhythm works best when it travels in this direction across an image but this doesn't have to be the case and it can also travel in a vertical direction.
Although the rhythm image above is not a great example I feel I have a better understanding of both pattern and rhythm following this exercise.