Merlin's Hat


Copyright 2016 Rich Widows

Approaching an Asymptote

The lines in the adjoining image, if extended, would continuously converge but never touch each other. In tech lingo, they would grow "asymptotically close" to each other without ever quite intersecting (although they would need to get substantially slimmer).

The "Approaching an Asymptote" image was a result of a mathematical profitability model created by Rich Widows for a investment industry product he helped develop. The model was based on an assumption that the classic economic "supply/demand" trade-off is essentially based on logarithmic rather than linear price-quantity relationships.

ASYMPTOTIC ART   from Rich's Algorithmic Art creations

UNWORLDLY IMAGES  from the computer of Richard Widows

The complex green extensions extending from the body of the image at left seem to disappear. In reality, they diminish at a constant rate and get so small that they appear to vanish. If sufficiently magnified, they would be identical in color and design to every other portion of that particular segment. Because they only change "forever" in size, but not in shape or design, they can accurately described as asymptotes because the ratios of edges to the midpoint of the extensions remains constant---forever (at least to infinity!).


An interesting  "fracrtal-asymptote" construct

The image at left represents an interesting example of an asymptote. If the image were to be vertically elongated to any distance, its right and left extremities would continuously approach its middle, but never touch the center or each other.  Also, suppose the image is elongated to the point where its thickness diminishes to a small fraction of a millimeter. That tiny slice of it, if sufficiently enlarged, would look exactly like the image that appears on this page.  Many “fractal” constructs exhibit this tendency to present the same image independent of the size or location of the sample that’s viewed. In that respect, such fractal constructs exhibit that would seem to indicate infinite scalability.