Thompson transformations parametric warping based on quadrat

Thompson transformations (parametric “warping” based on quadratic functions, Wilkinson, 2005, pp. 223–224) as illustrated in Figure 3 allow positive and negative transformations based on parameters P1–P10. Of these, the presented generative system uses the six parameters P1, P2, P3, P6, P7 and P8. Parameters P4, P9 and P10 are ignored while P5 can be toggled manually, providing an “italics” option. Parametric input for the six Thompson transformations performed by the system is derived from the ASCII bit patterns of characters of a “private key” string, which is “rotated” by three characters with each input keystroke. Any ASCII string of any length can be used for this telomerase inhibitor purpose (Figure 6). Once a key is pressed, the first three characters of the “private key” string are converted to their respective ASCII bit patterns and the six last bits of each are used to produce two factors out of the set −4, −3, −2, −1, 1, 2, 3, 4, which are multiplied with a scaling factor (0.075 gives a good effect) to produce a total of six parameters (see Figure 4). Following parametric Thompson transformations, the resulting glyph outline curves are simplified by reducing their numbers of control points, resulting in casual looking, “blobby” glyphs. These are variant with identical characters being shown as different glyphs (see the bottom line of Figure 7). Overall, the resulting types are nevertheless largely consistent and recognisable as members of the same typographical style, which I call Polymorph. The generative system includes a rudimentary automatic kerning function, the performance of which is also visible in the bottom line of Figure 7. The top line of Figure 5 shows the typeface Helvetica. The middle line shows the hand-drawn, Helvetica-inspired typeface YWFT HLLVTKA Round, each character of which looks irregular, while identical characters are rendered with the same glyphs.
Observations Some processes are linear, predictable and seem causal while others involve circularity appear unpredictable. The difference can be shown with the distinction between the trivial machine and the non-trivial machine. Like the Enigma machine, instances of designing can be viewed as circular systems (Glanville, 1992; Fischer, 2010; Gänshirt, 2011, p. 79) which display the structure and quality of the non-trivial machine. It was demonstrated here that circular re-entry affecting the internal state of a system is a sufficient condition of indeterminability, and for systems characterised by circular re-entry to transcend the narrow notion of linear cause and effect typically applied to (digital) technology and natural-scientific research. The wonder and surprise offered by indeterminable systems depend on their interior workings evading observation (Fischer, 2008). Design is, on the inside, concerned with what is unpredictable to outsiders. It hence corresponds to the non-trivial machine. Science, always on the outside, is concerned with prediction and hence corresponds to the trivial machine. This poses a challenge to scientific researchers aiming to research into designing objectively, somewhat comparable to the challenge of cryptography that leaves outsiders mystified while insiders understand. Design processes can be appreciated and understood on the subjective inside. Objective scientific description, though, is required to approach design from the outside. The human mind is different in this respect (and obviously in other respects, too). It has the capability of accepting previously not accepted inputs, and of expressions beyond the range of expected outputs as illustrated by the statement “2 × 2=grün”. More overtly, nonetheless evident in human learning, the mind also modulates its repertoire of internal attitudes towards inputs it encounters, i.e. its range of internal states. In other words, our nervous system has the capability of amplifying the variety of ranges of inputs it accepts, of its internal states, and of outputs it can be expected to offer. The TM׳s, the NTM׳s and the Enigma machine׳s clearly specified, constant input, internal state, and output varieties are typical of digital technology (Fischer, 2011), which is developed and used precisely for the predictable control it offers, at the expense, as Glanville (2009, p. 119) argues, of variety. Fixes varieties in technical systems are established by a kind of observer (matchmaker) who intentionally brings system together to serve purposes by way of control (Fischer, 2011). The human mind, in contrast, can actively modulate these varieties. It can, for instance, refuse to answer a yes-or-no question in those terms or answer an arithmetic problem by naming a colour. Giving a human an arithmetic problem to solve implicitly aims to reduce that humans input and output variety to the language of arithmetic and numbers within which a response may then be evaluated. A humans concession to answer in terms of mathematics and numbers constitutes a reduction of that humans output variety. A surprising (i.e. substantially or formally incorrect) answer will then likely be dismissed as wrong, regardless of whether the contemplations that led to it have value. On such grounds Dostoyevsky׳s (2009, p. 25) underground man can be dismissed when he states: “I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too.”