Fractal Fingers
As bizarre as the branching fractal fingers of the Saffman-Taylor instability look, they’re quite a common phenomenon. In his video, Steve Mould demonstrates how to make them by sandwiching a viscous liquid like school glue between two acrylic sheets and then pulling them apart. The more formal lab-version of this is the Hele-Shaw cell, which he also demonstrates. But you may have come across the effect when pealing up a screen protector or in dealing with a cracked phone screen. In all of these cases, a less viscous fluid — specifically air — is forcing its way into a more viscous fluid, something that it cannot manage without the fluid interface fracturing. (Video and image credit: S. Mould)
![Preface
L-systems are a mathematical formalism which was proposed by Aristid Lindenmayer in 1968 as a foundation for an axiomatic theory of development. The notion promptly attracted the attention of computer scientists, who investigated L-systems from the viewpoint of formal language theory. This theoretical line of research was pursued very actively in the seventies, resulting in over one thousand publications. A different research direction was taken in 1984 by Alvy Ray Smith, who proposed L-systems as a tool for synthesizing realistic images of plants and pointed out the relationship between L-systems and the concept of fractals introduced by Benoit Mandelbrot. The work by Smith inspired our studies of the application of L-systems to computer graphics. Originally, we were interested in two problems:
• Can L-systems be used as a realistic model of plant species found in nature?
• Can L-systems be applied to generate images of a wide class of fractals?
It turned out that both questions had affirmative answers. Subsequently we found that L-systems could be applied to other areas, such as the generation of tilings, reproduction of a geometric art form from East India, and synthesis of musical scores based on an interpretation of fractals. This book collects our results related to the graphical applications of 1systems. It is a corrected version of the notes which we prepared for the ACM SIGGRAPH '88 course on fractals. [...]](https://media.ciberlandia.pt/ciberlandia-media/media_attachments/files/114/359/648/324/216/418/original/5afad812e0de7c99.png "Preface
L-systems are a mathematical formalism which was proposed by Aristid Lindenmayer in 1968 as a foundation for an axiomatic theory of development. The notion promptly attracted the attention of computer scientists, who investigated L-systems from the viewpoint of formal language theory. This theoretical line of research was pursued very actively in the seventies, resulting in over one thousand publications. A different research direction was taken in 1984 by Alvy Ray Smith, who proposed L-systems as a tool for synthesizing realistic images of plants and pointed out the relationship between L-systems and the concept of fractals introduced by Benoit Mandelbrot. The work by Smith inspired our studies of the application of L-systems to computer graphics. Originally, we were interested in two problems:
• Can L-systems be used as a realistic model of plant species found in nature?
• Can L-systems be applied to generate images of a wide class of fractals?
It turned out that both questions had affirmative answers. Subsequently we found that L-systems could be applied to other areas, such as the generation of tilings, reproduction of a geometric art form from East India, and synthesis of musical scores based on an interpretation of fractals. This book collects our results related to the graphical applications of 1systems. It is a corrected version of the notes which we prepared for the ACM SIGGRAPH '88 course on fractals. [...]")
