Applications of Fractals and Chaos: The Shape of Things by A.J. Crilly, Rae Earnshaw, Huw Jones

By A.J. Crilly, Rae Earnshaw, Huw Jones

Applications of Fractals and Chaos offers new advancements during this rapidlydeveloping topic sector. The presentation is greater than only theoretical, it in particular provides specific functions in quite a lot of purposes parts. lower than the oceans, we think about the ways that sponges and corals develop; we glance, too, on the balance of ships on their surfaces. Land itself is modelled and functions to paintings, medicineand camouflage are awarded. Readers should still locate basic curiosity within the diversity of components thought of and will even be capable of become aware of equipment of worth for his or her personal particular components of curiosity from learning the constitution of similar activities.

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In some cases, seven or eight spicules meet in one point, and septagons and octagons are formed. In an idealized version of the triangular network, it is transformed into a network of five- or six-sided polygons by removing some of the skeleton elements which meet at one point. The result of this transformation is a Haliclona oculata-like network (see [Kaan91b]). As becomes clear in the next sections, Haliclona simulans is a good case study for a model where the objects are represented in the iteration process by layers of 46 Jaap A.

A typical characteristic of many modular organisms is that they often exhibit a wide range of growth forms, caused by differences in the physical environment. It is often possible to arrange the growth forms along a physical gradient; the forms gradually transform into each other with the changing environmental parameter. An example of such a range, of a modular organism with radiate accretive growth, is shown in Figure 2. Basically, the growth forms of the displayed species, the sponge Haliclona oculata, range from quite regular, thin-branching to irregular plate-like forms.

The process is repeated to obtain quarter, eighth, sixteenth, ... reductions. The yardstick for the various reductions, €, is thus expressed as a power function of 2£, with· € = 0, 1,2,3, ... representing zP,ro, half, quarter, eighth, ... reductions of the beats. Using this method and working again on Bach's music, notes are translated into visual signals (Figure 4). The 'irregularities' of the original music landscape are smoothed out through successive reductions. The total number of note intervals is correspondingly less.

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