Generalization gradient shape and summation in steady-state tests.

The team worked with pigeons in a small lab chamber.

Birds pecked a disk for food when certain colors of light appeared.

After training, the researchers tested many nearby colors to map how responding spread.

They kept each test going until pecking stayed flat for many minutes.

The birds made smooth, hill-shaped curves around the trained color.

When two trained colors sat close together, the curves added up in the middle.

The shape matched a simple math rule, like stacking two small hills into one bigger hill.

Hoffman et al. (1966) saw the same stacking effect with tones and mild shock.

Their pigeons also showed two peaks that merged, giving early proof the rule works across setups.

Okouchi (2003) moved the test to college students looking at line lengths.

People gave the same lopsided hills, showing the pattern is not just for birds.

HOFFMAN et al. (1963) showed that these hills can last years but fade with repeated tests.

Together the four papers say: gradients form fast, add up predictably, survive a long time, and hold across species.

You can plan stimulus sets knowing that nearby cues will blend.

If you teach two similar colors, responses will grow in between without extra work.

Pick spacing that lets the hills overlap for smooth transfer, or separate targets to keep them distinct.