The Compressive Curve Becomes the Reflex

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

The Compressive Curve Becomes the Reflex

A light-following Braitenberg vehicle steers on an LDR whose resistance follows R = R_ref × (E / E_ref)^-γ, with R_ref = 10 kΩ at 10 lux and γ = 0.7, fed through a 3.3 V divider. The chapter warns that near a lamp this curve compresses the vehicle’s own steering signal — 900 and 1000 lux can produce nearly the same output, leaving the vehicle indecisive. This audit asks the question that compression invites: exactly how much steering voltage does each 10× jump in light still deliver once the sensor is close to the lamp?

Companion to the chapter Braitenberg Transfer Tuning — every number here comes from that chapter.

Ada: This chapter makes a strong claim – that equal 10x jumps in light produce shrinking signal steps – and it is worth carrying the power law and the divider at full precision to see exactly how much the vehicle’s reflex dulls near the lamp. The LDR follows R = R_ref x (E / E_ref)^(-gamma) with R_ref = 10 kohm at 10 lux and gamma = 0.7:

  • At 100 lux: 10 kohm x (100/10)^-0.7 = 10 kohm x 10^-0.7 = 10 kohm x 0.199526 = 1.9953 kohm
  • At 1000 lux: 10 kohm x (1000/10)^-0.7 = 10 kohm x 100^-0.7 = 10 kohm x 0.039811 = 0.3981 kohm

Each 10x brighter step multiplies resistance by the same 0.1995, but the resistance change shrinks: 10 - 1.9953 = 8.005 kohm then 1.9953 - 0.3981 = 1.597 kohm, matching the chapter’s 8 kohm and 1.6 kohm. Now feed that into the divider Vout = 3.3 V x 10 kohm / (R_ldr + 10 kohm):

  • 10 lux: 3.3 x 10 / (10 + 10) = 1.6500 V
  • 100 lux: 3.3 x 10 / (1.9953 + 10) = 2.7511 V
  • 1000 lux: 3.3 x 10 / (0.3981 + 10) = 3.1737 V

The conditioned signal steps are 2.7511 - 1.6500 = 1.101 V for the first 10x and only 3.1737 - 2.7511 = 0.423 V for the second – the chapter’s 1.10 V then 0.42 V. The design-meaningful conclusion is that the vehicle’s steering authority is not a fixed gain: the same 10x change in light delivers less than half the voltage swing once the lamp is close, so the compressive sensor curve, not any line of code, is what makes the vehicle lunge in the dark and crawl in the light.

Every number above is taken from the chapter’s own material and re-derived step by step.