Fractal Fingers

[Eliecer Brathwaite]

Withthe right balance of viscosity and surface tension, many fluid combinations can form fractal or dendritic patterns. Here, researchers use a drop of food coloring atop a mixture of water and xanthan gum. Depending on the concentration of gum (and the age of the viscous fluid) different fractal patterns spread quickly across the surface. (Image and video credit: R. Camassa et al.)

Dyed isopropyl alcohol atop a thin layer of acrylic medium spreads in a fractal fingering pattern. Although the shapes are reminiscent of the viscous fingers seen in in the Saffman-Taylor instability, these patterns are most likely a result of surface tension. The lower surface tension of the alcohol causes Marangoni forces to pull it outward. The branching shapes indicate an instability, likely driven by surface tension, but the details of the mechanism behind it are unclear. (Image credits: J. Nahabetian)

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

What happens when one attempts to push water through a fluid of higher viscosity? Under appropriate experimental conditions, the water breaks through in the form of highly branched patterns called viscous fingers. Water was used to push a more viscous but miscible, non-newtonian fluid in a Hele-Shaw cell. The resulting viscous finger instability was found to be a fractal growth phenomenon. Reproducible values of the fractal dimension df were found and were interpreted using a modification of the diffusion limited aggregation model.

Second, and this strikes me the most, in each iteration the area of the tree (the black region) is reduced by a factor of 5/9. So, for example, after just six iterations the area of the initial square is reduced to only 3% of its original area! However, the perimeter of the whole shape always stays the same. Essentially, this means that the final Vicsek fractal is made of infinitely thin threads that make up its structure. Similarly for the Sinai desert fingers, although we can see the general shape and patterns at the 2km scale, once we zoom in further and further, a threaded structure is revealed.

This site, like many others, uses small files called cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we'll assume that you are happy to receive all cookies on this website (Cookie Policy). However, if you would like to, you can change your cookie settings at any time.

How to place down, lift and move your fingers in a way that minimises fatigue, by Alex Henery, principal double bassist of the Sydney Symphony and head of double bass studies at the Sydney Conservatorium of Music. From February 2019

The effect of fractal fingering can be observed if a droplet of an ink-alcohol mixture is deposited onto diluted acrylic paint. How are the geometry and dynamics of the fingers influenced by relevant parameters?

A light sphere with a conducting surface is suspended from a thin wire. When the sphere is rotated about its vertical axis (thereby twisting the wire) and then released, it starts to oscillate. Investigate how the presence of a magnetic field affects the motion.

When a compact disc or DVD is illuminated with light coming from a filament lamp in such a way that only rays with large angles of incidence are selected, a clear green line can be observed. The colour varies upon slightly changing the angle of the disc. Explain and investigate this phenomenon.

When a stream of water hits a rigid metal mesh within a range of angles, a whistling tone may be heard. Investigate how the properties of the mesh, stream and angle affect the characteristics of the sound produced.

Secure the lower ends of two identical leaf springs to a non-magnetic base and attach magnets to the upper ends such that they repel and are free to move. Investigate how the movement of the springs depends on relevant parameters.

A droplet of less viscous liquid floating in a bath of a more viscous liquid develops surprising wave-like patterns when the entire system is set into vertical oscillation. Investigate this phenomenon and the parameters relevant to the production of stable patterns.

Take a thick plate of non-magnetic material and fix a neodymium magnet on top of it. Suspend a magnetic rod (which can be assembled from cylindrical neodymium magnets) underneath it. Deflect the rod so that it touches the plate only with highest edge and release it. Study the motion of such a pendulum under various conditions.

When placed on its side on a ramp and released, a screw may experience growing oscillations as it travels down the ramp. Investigate how the motion of the screw, as well as the growth of these oscillations depend on the relevant parameters.

Sprinkle light particles on a water surface. Then allow a water stream to be incident on the surface from a small height. Under certain conditions, the particles may begin to move up the stream. Investigate and explain this phenomenon.

A ferrite rod is placed at the bottom end of a vertical tube. Apply an ac voltage, of a frequency of the same order as the natural frequency of the rod, to a fine wire coil wrapped around its lower end. When a ball is placed on top of the rod, it will start to bounce. Explain and investigate this phenomenon.

Take a vessel and pour some granular material into it, for example, rice. If you dip e.g. a spoon into it, then at a certain depth of immersion, you can lift the vessel and contents by holding the spoon. Explain this phenomenon and explore the relevant parameters of the system.

A glass tube with a sealed top is filled with water and mounted vertically. The bottom end of the tube is immersed in a beaker of water and a short segment of the tube is heated. Investigate and explain the periodic motion of the water and any vapour bubbles observed.

Place a few balls in a round container. If you move the container around a vertical axis, the balls can move co-directionally with the movement of the container, or they can move in the opposite direction. Explain this phenomenon and investigate how the direction of movement depends on relevant parameters.

A piston placed in the open end of a horizontal test tube which has its other end partially filled with steel wool may oscillate when the closed end is heated up. Investigate the phenomenon and determine the efficiency of this engine.

A sand-filled lane results in the dissipation of the kinetic energy of a moving vehicle. What length is necessary for such an arrester bed to entirely stop a passively moving object (e.g. a ball)? What parameters does the length depend on?

The site is secure.

The ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Methods: The study included 48 patients who underwent the RPE procedure. Study groups were as follows: group 1 (successful conventional RPE [n = 24, 5 male and 19 female patients; mean age standard deviation, 15.85 0.97 years]) and group 2 (failed conventional RPE [n = 24, 5 male and 19 female patients; mean age standard deviation, 15.96 1.08 years]). Fractal dimension (FD) analysis was conducted on hand-wrist radiographs of the patients for 4 different regions: the epiphysis-diaphysis line of the radius bone and the proximal, medial (MP3), and distal (DP3) phalanxes of the middle finger. A Student t test was performed to compare fractal values between the groups. A receiver operating characteristic analysis was applied to determine the optimal cutoff value of FDs. In addition, a Pearson correlation coefficient was calculated to evaluate the relationship between the fractal values and either age or hand-wrist stage in a second sample group (n = 90; age range, 8.7-18.7 years).

Inspired by social media, image-sharing sites and online tutorials, Calhoun decided she wanted to try a trend made popular through the internet: wood fracking, also known as Lichtenberg wood-burning or fractal wood-burning. This wood-working method includes using high volts of electricity to essentially shock Lichtenberg patterns into wood, which some say, against expert advice, can be achieved with a microwave transformer or a car battery.

The machine, which sat on the floor, was turned off when she picked up the cables, but when she went to take a step, she tripped on her pajama pants and accidentally turned it on. The electricity coursed through her hands, keeping her body upright and locked in a standing position. She was unable to let go of the cables or move away from the machine.

When the paramedics arrived, they understood that Calhoun needed emergency treatment and the specialty care of a burn center. So, she was life-flighted from Tennessee to Burn and Reconstructive Centers of America (BRCA), providing services at WellStar Cobb Hospital in Austell, GA. There she was given preliminary treatment, but the question was: how much of her hands could they save?

To give her hands the best outcome possible, she was transferred to the headquarters of BRCA and the largest burn center in the country, the Joseph M. Still Burn Center at Doctors Hospital, where she was treated by burn and reconstructive surgeon Dr. Piotr Skowronski. Dr. Skowronski salvaged as much of her fingers as the necrotic tissue allowed, including saving the primary function of her hand by reconstructing her thumb.

Though this may seem like a worst-case scenario, Calhoun is incredibly lucky. In recent years, there have been several deaths attributed to wood fracking and homemade Lichtenberg machines. Electricity burns can be some of the most complex burn injuries to treat, often leading to deep tissue, muscle and nerve damage, organ damage and amputation.

3a8082e126