Inks which show variance in color and darkness as you write are called shading inks and are very popular as a subset of bottle ink. Looking at the example of a shading ink above*, notice how the spots where the pen naturally lingers are the darkest parts of the word, that is typical of shading ink.
Shading inks are generally less saturated than the non shading inks and that means they do not contain an ultra high dye concentration and resemble antique ink more than the highly saturated modern inks.
The wider your nib, the more the variation in color when writing with a shading ink, so if you want to see the maximum of what an ink can do, then use a broad or italic (stub) nib and admire the result.
All colors, even black, can have a shading effect. Iron gall inks were famous for their shading characteristics, but the color range was pretty limited (usually a blue-black).
Nowadays, there are lots of shading inks in the marketplace. Noodler’s Golden Brown and Apache Sunset are two famous ones (brown and yellow-to-orange respectively). Diamine Meadow is a lovely true green which can shade to yellow, Montblanc Black can go from jet black to a dark grey, and Akkerman Shocking Blue shades and has a reddish metallic cast to it when it dries.
If you are looking for a good recommendation on shading inks for your fountain pen, try going to The Fountain Pen Network and searching for “shading ink”, you are sure to find a great many. There is a link to The Fountain Pen Network to the right of this blog. Happy hunting!
*The name of the pictured ink is “Black Swan in North African Violets” and you have to make it yourself out of two different Noodler’s inks. Searching for it on The Fountain Pen Network will point the way to the recipe.