I have a Canon 10D DSLR. Sometimes I get weird patterns in my pictures. What causes this pattern, and how can I eliminate or prevent it?

I have a Canon 10D DSLR. Sometimes I get weird patterns in my pictures. What causes this pattern, and how can I eliminate or prevent it?

I might be wrong, but unfortunately I think that is just the pattern of your sensor's noise, meaning sensitivity of your sensor was so high, it captured byproduct of it's overheating.
This happens because camera wants to compensate for low light, making sensor more sensitive to capture more details. Sensitivity of a sensor is regulated by ISO, higher the ISO, higher the noise.
This is normal and every camera has this when using too high ISO. Only way to fix that is shooting in conditions with more light, so your camera doesn't have to use high ISO.
If you take a picture in conditions with more light, but the problem persists, then it might be a problem with the sensor.
I found this problem fascinating enough to research a suitable answer.
1) This is NOT Moire interference; as was mentioned above, the grid is far too regular (in both vertical and horizontal direction.
2) This is also NOT noise banding resulting from working the sensor too hard. The banding, again, is far too regular and nothing in the image suggests an unusual exposure which, in fact, looks pretty typical.
3) Some internet sleuthing suggests that this " Grid Banding" processing artifact plagues a few generations of Canon CMOS sensors, going as far back as 2008 and the 5D Mark II (see this link for a cursory description: https://blog.kareldonk.com/canon-eos-5d-mark-ii-barely-worth-it/. According to several users, this grid banding shows up in relatively underexposed parts of an image at fairly low ISO (like the OP's image) and is even worse when recording video.
This link (http://www.dvxuser.com/V6/archive/index.php/t-207542.html) describes a 7D users experience with this problem and what Canon did to repair this "unbalanced A/D channels" issue....at least partially. Apparently, there is no "user error" in creating this artifact, it is a known issue with Canon CMOS sensors, and may be repairable by Canon, or at least partially mitigated.
I believe this is what's called a Moiré Pattern. That's when two patterns--the background you're shooting and the camera's sensor--are overlaid and produce a third pattern. I'm guessing the background has some sort of texture that doesn't line up with the camera's sensor pattern, so in some places the sensor picks up the pattern and in others, it doesn't, thus producing the Moiré pattern. It's worth noting that the Canon 10D had a resolution of 6.3 Megapixels, which may be course enough to produce some Moiré patterns.
If the background in question did not have any pattern or texture, however fine, then this is wrong. If so, I can retract it.