Macro

1. 01

   The set

   Each pixel is a complex number $c$. Starting from zero, iterate $z \to z^2 + c$: inside the set the orbit stays bounded, outside it escapes, and the colour says how fast. The camera heads for the ringed point.

2. 02

   The zoom runs on trading time

   The camera advances with cumulative realised variance, not with the calendar (dashed): calm years barely move it, crises make it jump. 19 October 1987 alone is 4% of the clock since 1985.

3. 03

   Colour is volatility

   Each day’s 21-day volatility, ranked against the whole history: blue when markets are calm, magenta and orange under stress. The same strip runs under the chart above.

4. 04

   Every scale looks alike

   After the last close the window shrinks to the last 10 trading days while the zoom grows by the same factor. Prices are rescaled by $w^H$, where $w$ is the window’s length and $H$ = 0.5 is estimated from the index, so every window looks equally rough.

The set is computed live in the browser, zooming towards the Misiurewicz point $c \approx -0.77568 + 0.13647\,i$ down to ×10¹⁰. The S&P 500 is not a fractal in this sense: what the two share is structure across scales. Data: S&P 500 daily closes, Yahoo Finance (ticker ^GSPC).