Chaotic sequences

From the illustrations to James Gleick's Chaos: Making a New Science, 1987.

There are two kinds of beauty: free beauty (pulchritudo vaga), or beauty which is merely dependent (pulchritudo adhaerens). The first presupposes no concept of what the object should be; the second does presuppose such a concept and, with it, an answering perfection of the object. Those of the first kind are said to be (self-subsisting) beauties of this thing or that thing; the other kind of beauty, being attached to a concept (conditioned beauty), is ascribed to objects which come under the concept of a particular end.

Flowers are free beauties of nature. Hardly anyone but a botanist knows the true nature of a flower, and even he, while recognizing in the flower the reproductive organ of the plant, pays no attention to this natural end when using his taste to judge of its beauty. Hence no perfection of any kind — no internal purposiveness, as something to which the arrangement of the manifold is related — underlies this judgment. Many birds (the parrot, the hummingbird, the bird of paradise), and a number of crustaceans, are self-subsisting beauties which are not appurtenant to any object defined with respect to its end, but please freely and on their own account. So designs à la grecque, foliage for framework or on wallpapers, etc., have no intrinsic meaning; they represent nothing — no object under a definite concept — and are free beauties. We may also rank in the same class what in music are called fantasias (without a theme), and, indeed, all music that is not set to words.

--Immanuel Kant, Critique of Judgment, paragraph 16.