Broaden-and-Build: Upward & Downward Emotional Spirals

Emotional Climate

Positivity ratio (pos:neg) 2.9 : 1

Stressor intensity 1.0×

Broadening practice (savoring / gratitude) 1.0×

Event pace 1.0 / s

Live State

— Stable —

Resources R

30.0

Wellbeing mood

+0%

Repertoire breadth W

0.30

Realized ratio

—

How it works

Barbara Fredrickson's broaden-and-build theory proposes that momentary positive emotions broaden a person's momentary thought-action repertoire (breadth W), and that broadened states build durable psychological/social resources (R) — which in turn buffer against future negative events and make further positive emotion more likely. That feedback loop is an upward spiral; running it in reverse (few positive events, unbuffered stressors) is a downward spiral.

event valence:  P(positive) = ratio / (ratio + 1)

positive event (impact i):
  W += broaden · i · (1 − W)
  R += buildGain · i · (0.4 + W)

negative event (impact i · stress):
  damage = (i · stress) / (1 + R / Rk)   ← resources buffer damage
  R -= damage
  W -= 0.4 · i · (1 − Rk-buffer)

continuous decay each step:
  R → R − decayRate · R · dt   (resources fade without reinforcement)
  W → W − forgetRate · W · dt
  mood M is an exponential moving average of recent valence

Positivity ratio sets how often events are drawn positive vs negative — 2.9:1 is the informal "flourishing" benchmark from the positive-psychology literature.
Stressor intensity scales the damage of negative events before buffering.
Broadening practice models an intervention (gratitude journaling, savoring, mindfulness) that amplifies how much each positive event builds W and R.
The resource cloud's particle count and the central core's pulse both track R and W live — a shrinking, dim cloud is a downward spiral; a swelling, bright one is an upward spiral.

Positive event Negative event Resource particle

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