Computer worms are similar to viruses in that they replicate functional copies of themselves and can cause the same type of damage. In contrast to viruses, which require the spreading of an infected host file, worms are standalone software and do not require a host program or human help to propagate.
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This is a specific type of malware that spreads itself once it’s initially run. It's different from other types of malware because it can either be like a parasite that attaches to good files on your machine, or it can be self-contained and search out other machines to infect.                                         
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Think of inchworms rather than tapeworms. These are not parasitic worms, but the kind that move around on their own. In the malware sense, they're viruses that are self-contained (they don’t attach themselves like a parasite) and go around searching out other machines to infect.