[OC] Logistic Curve Windmills Visualization

What This Visualization Shows

This data visualization displays "[OC] Logistic Curve Windmills" and provides a clear visual representation of the underlying data patterns and trends. The visualization focuses on I was playing with the logistics curve fractal, plotted it out to both negative and positive extents - it’s relatively straightforward if maths is your thing, I decided that I thought one arm of the logistics curve looked like a windmill blade, and I wondered what it would look like if I completed the pattern, by mirroring and duplicating the curve at 45 degree turns, so 8 arms in all.

And finally, wrapped in a circle with standard COS and SIN functions.

The “n” at the top of the page are scaling factors applied to each cross, they warp and size the two crosses, set in the sheet to randomise. There is an infinite number of these patterns that can be created.

The plot is straightforward scatter plot, markers only, the default circle reduced to point size 2 (the smallest) and border remove, coloured dark grey with 80% transparency.

I really love how it looks almost hand drawn, it’s the overlapping points across the 8 curves along with the 80% transparency, very much like say cross hatching pencil drawing to introduce shade

This is for the curve itself, let me know if you’d like me to provide rest of details for the plot, but just as described.

\`\`\`\` Excel

=LET(

λMin, -2,

λMax, 4,

λSteps, 3500,

x0, 0.5,

burnIn, 400,

keep, 80,

blowup, 1E6,

lambdas, SEQUENCE(λSteps, 1, λMin, (λMax-λMin)/(λSteps-1)),

orbit, LAMBDA(λ, SCAN(

x0, SEQUENCE(burnIn+keep,1),

LAMBDA(prev,\_, LET(

next, λ\*prev\*(1-prev),

IF(ABS(prev)>blowup, NA(), next)

)))),

tail, LAMBDA(col, TAKE(col, -keep)),

pts, DROP(

REDUCE({0,0}, lambdas,

LAMBDA(acc, λ, LET(

xs, tail(orbit(λ)),

VSTACK(acc, HSTACK(λ+0\*xs, xs))

))

),1),

pts

), which allows us to understand complex relationships and insights within the data through visual storytelling.

Deep Dive into the Topic

This data visualization represents a sophisticated analysis of complex information patterns that provide valuable insights into underlying trends and relationships. Data visualization serves as a bridge between raw numerical data and human understanding, transforming abstract statistics into comprehensible visual narratives.

The power of data visualization lies in its ability to reveal patterns, outliers, and correlations that might not be apparent in traditional tabular formats. Through careful selection of chart types, color schemes, and interactive elements, effective visualizations can communicate complex information quickly and accurately to diverse audiences.

Modern data visualization combines statistical analysis with design principles to create compelling visual stories. This interdisciplinary approach requires understanding both the underlying data and the cognitive processes involved in visual perception. The result is more effective communication of quantitative insights that can inform decision-making and drive positive change.

Data Analysis and Insights

The patterns revealed in this visualization demonstrate the importance of systematic data analysis in understanding complex phenomena. By examining different data segments, time periods, and categorical breakdowns, we can identify trends that inform strategic planning and decision-making processes.

Statistical analysis of this data reveals variations across different dimensions that provide insights into underlying drivers and relationships. These patterns help identify areas of opportunity, potential risks, and key performance indicators that can guide future actions and resource allocation.

The analytical approach used in this visualization enables comparison across different categories, time periods, or geographic regions, revealing insights that support evidence-based decision-making. This type of analysis is essential for organizations seeking to optimize performance and understand complex market dynamics.

Significance and Applications

This data visualization has important implications for understanding trends and patterns that affect decision-making across multiple sectors. The insights derived from this analysis can inform policy development, business strategy, resource allocation, and operational improvements.

For analysts, researchers, and decision-makers, this type of data visualization provides essential insights for strategic planning and performance optimization. Whether addressing operational challenges, market analysis, or policy development, understanding data patterns helps create more effective strategies and solutions.

The broader significance lies in how this information contributes to our understanding of complex systems and relationships. This knowledge helps predict future trends, identify potential challenges, and develop more informed approaches to problem-solving and opportunity identification.