• Pixel-art Flickermoth, the Pink-Noise Moth Queen, on a black mug with the slogan "AVERAGING LONGER. REGRETTING LONGER."

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Flickermoth, the Pink-Noise Moth Queen Mug

\[S(f) \propto \frac{1}{f^{\alpha}}, \qquad \alpha \approx 1\]
$21.99 USD
$21.99 USD
Rea Slutsåld
Size

Flicker (1/f) noise: spectral density S(f) ∝ 1/fα with α ≈ 1. When the fluctuating quantity is fractional frequency y (flicker FM, Sy(f) ∝ 1/f), the Allan deviation stops falling and flattens into a floor, σy(τ) = const, so averaging longer stops helping; for white FM it falls as τ−1/2.

The joke: With white noise σ falls as 1/√τ; with 1/f it plateaus, so the extra 6 hours of averaging bought nothing. The slogan on the mug reads AVERAGING LONGER. REGRETTING LONGER.

Source: J. B. Johnson, Phys. Rev. 26, 71 (1925) (low-frequency 'flicker effect'); D. W. Allan, Proc. IEEE 54, 221 (1966).

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Flicker (1/f) noise: spectral density S(f) ∝ 1/fᵅ with α ≈ 1. When the fluctuating quantity is fractional frequency y (flicker FM, S_y(f) ∝ 1/f), the Allan deviation stops falling and flattens into a floor, σ_y(τ) = const, so averaging longer stops helping; for white FM it falls as τ⁻¹ᐟ².

The joke: With white noise σ falls as 1/√τ; with 1/f it plateaus, so the extra 6 hours of averaging bought nothing. The slogan on the mug reads AVERAGING LONGER. REGRETTING LONGER.

Source: J. B. Johnson, Phys. Rev. 26, 71 (1925) (low-frequency 'flicker effect'); D. W. Allan, Proc. IEEE 54, 221 (1966).

Equations

\[S(f) \propto \frac{1}{f^{\alpha}}, \qquad \alpha \approx 1\]
\[S_y(f) \propto \frac{1}{f} \;\Rightarrow\; \sigma_y(\tau) = \text{const}\]
\[\text{white FM: } \sigma_y(\tau) \propto \tau^{-1/2}\]
SymbolMeaningUnit
\(S(f)\) noise power spectral density —
\(f\) Fourier frequency \(\mathrm{Hz}\)
\(\alpha\) spectral exponent —
\(y\) fractional frequency —
\(\sigma_y(\tau)\) Allan deviation —
\(\tau\) averaging time \(\mathrm{s}\)

Sources

  1. J. B. Johnson, Phys. Rev. 26, 71 (1925) (low-frequency 'flicker effect')
  2. D. W. Allan, Proc. IEEE 54, 221 (1966)

Field notes

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