# Modular Form ii

This is a continuation of ideas from before, except we now embrace color. But we don't use the typical colors.

A modular form impersonating a stage curtain. DLD Oct 2020.

A complex-valued function $$f: \mathbb{C} \longrightarrow \mathbb{C}$$ naturally has a four dimensional graph. We represent this in two dimensions here by representing each point $$z$$ in the codomain by $$z = r e^{i \theta}$$, for a magnitude $$r$$ and argument $$\theta$$. Here, we choose colors based on $$\theta$$, and we encode the magnitude in a variety of ways.

Sometimes we use contours in indicate the magnitude.

Blown snow. DLD Oct 2020.
Glacial sliding. DLD Oct 2020.

Or we use darkness or lightness to indicate the magnitude.

Glowing orb. DLD Oct 2020.
$\Delta(z)$ in yellow, blue, and black. DLD Oct 2020.

Choosing small windows, various forms of self-similarity make themselves obvious. These images have a flow much like the surface of a stream. Colors swirl in eddies and whirlpools.

Flickering flame. DLD Oct 2020.
Wind over mountain peaks. DLD Oct 2020.

Small differences in color can have strong associative effect. The following image is essentially the same as Features in the mist i, from before, but with colors inverted and on a grey paper background.

Lit marble. DLD Oct 2020.

This is a modular form, but it looks like a speckled marble, perhaps a solar map.

Untitled modular form banner. DLD Oct 2020.
Untitled modular form medallion. DLD Oct 2020.
Lightning storm. DLD Oct 2020.
Untitled modular form detail. DLD Oct 2020.