Grid resampling

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Create a checkerboard grid of alternating black and white pixels (100x100). Resample to smaller nxn sizes by a Lanczos filter of radius 2 / (100 / n). This is a simple test for a resampling algorithm.

The original 100x100 grid.

The result for 99x99 (one valley).

Here is the result for 98x98 (two valleys).

Here is the result for 97x97 (three valleys).

You can see a pattern here (the number of valleys keep on incrementing) which continues predictably down until size 65x65, which is the last image showing more than one color. Here is the result for 65x65.

The result for 65x65.

I don't know how to explain the behaviour (leave me a post if you can!).