The second half of that sentence is not a complete sentence:
[T]he larger numbers from brighter patches.
There's no verb, so this would be a fragment. Therefore, we cannot use a semicolon or period to separate these two clauses. We must use a comma.
This would still be true if there were a verb; you can't do this kind of parallel structure proper justice with a period or a semicolon. However, such a construction would be more grammatical if it had a coordinating conjunction as well:
The smaller numbers come from darker patches, and the larger numbers come from brighter patches.
Leaving out the "and" would make it an ungrammatical comma splice, but replacing the comma with a semicolon would be the wrong fix, because it would interfere with the parallel structure of the sentence.
If you don't insert the extra verb, the original construction is also perfectly grammatical, because the second clause is a dependent clause with no verb.
To summarize:
- "The smaller numbers come from darker patches, the larger numbers from brighter patches." is a grammatical compound sentence, made up of an independent clause and a dependent clause.
- "The smaller numbers come from darker patches, and the larger numbers come from brighter patches." is a grammatical compound sentence, made up of two independent clauses and a coordinating conjunction.
- "The smaller numbers come from darker patches, and the larger numbers from brighter patches." is grammatical but a bit more awkward than (1).
- "The smaller numbers come from darker patches, the larger numbers come from brighter patches." is an ungrammatical comma splice. A semicolon would be legal in place of the comma, but (1) or (2) would be much more natural.