Lichtenberg Figures - Lightning as Art

8/8/2019 Lichtenberg Figures - Lightning as Art

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What are Lichtenberg Figures, and how do we create them?

(Last updated 07/20/09)

Doubly Irradiated "Windblown Lightning" Sculpture

This Captured Lightning sculpture was created by irradiating a block of clear acrylic with a beam

of electrons from a 5 million volt particle accelerator. The electron beam irradiated the left side,

the specimen was then rotated 180 degrees, and was irradiated once more on the opposite side.

This created two independent layers of electrical charge deep inside the specimen. The rightmost

charge layer was then manually discharged, creating a miniature "lightning storm" within the

layer above. Additional electrical discharges then grew between the right and left charge

layers, forming a beautiful 3D discharge pattern. This sculpture was lit from below by bluelight emitting diodes (LED's). Unlike common, low resolution laser crystal art, each of our

Captured Lightning sculptures contain a unique, and incredibly detailed, natural fractal

discharge pattern. No two sculptures are identical. As they branch, the branching discharge

channels become increasingly finer and hairlike, ultimately disappearing at the tips. The

smallest discharges are thought to extend to the molecular level.(Actual size: 3" x 3" x 2")
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What Are Lichtenberg figures?The scientific name for our Captured Lightning sculptures are "Lichtenberg Figures". Lichtenbergfigures are branching, tree-like or fern-like patterns that are created by high voltage discharges on thesurface of, or within, electrical insulating materials (dielectrics). The first Lichtenberg figures were actually2-dimensional patterns formed in dust on the surface of charged insulating plates in the laboratory oftheir discoverer, German physicist Georg Christoph Lichtenberg (1742-1799. Professor Lichtenberg

made this observation in the late 1700's, demonstrating the phenomenon to his physics students and peers.He reported his findings in his memoir: Super nova methodo naturam ac motum fluidi electriciinvestigandi (Gttinger Novi Commentarii, Gttingen, 1777). The basic principles involved in theformation of these electrostatic figures later evolved to become modern xerography and the science of

plasma physics. Lichtenberg used electrostatic devices to charge the surfaces of various insulating

materials such as resin, glass, or ebonite. He then sprinkled a mixture of finely powdered sulfur and redlead (lead tetroxide) onto the surface. The powdered sulfur was attracted to the positively charged regionsand the red lead to negative regions, thus making the previously hidden regions of charge clearly visible.

Lichtenberg observed that the shapes of the positively and negatively charged figures weresignificantly different. Positive figures tended to be star-like with long branches, while negative figurestend to be shorter, and round or fan-like. By carefully pressing a piece of paper onto the dusted surface, hewas able to transfer these image onto the paper, demonstrating what was later to become the processof Xerography. Drawings of positive and negative figures captured by Dr. Lichtenberg are shown below.

Positive Lichtenberg figure Negative Lichtenberg figure

Notable later researchers included Gaston Plant (mid 1850's), French artist and scientist EtienneLeopold Trouvelot and Thomas Burton Kinraide (late 1800's), Dr. Carl Edward Magnusson, and Dr.Arthur Von Hippel (1930's+). These later researchers used photographic film to directly capture thelight emitted by positive or negative high voltage discharges along dielectric surfaces. Dr. VonHippel discovered that Lichtenberg figures were actually created through complex interactions

between ionized gas (corona or electrical spark discharges) and the dielectric surface below. It was alsofound that increasing the applied voltage or reducing the surrounding gas pressure caused the length ofthe figures to increase. This property was used in klydonographs, special recording instrumentsthat photographically recorded the size and shape of Lichtenberg figures that appeared duringabnormal electrical surges on power lines.Klydonographs allowed lightning researchers and powersystem designers to estimate the peak voltage and polarity of abnormal high voltage transients causedwhen lightning struck power lines. A schematic diagram of the main parts of a klydonograph is shown onthe leftmost drawing below, along with examples of "klydonograms" from equal magnitude positive

and negative high voltage transients.
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is irradiated, huge numbers of electrons accumulate inside, creating a cloud-like layer of excessnegative electrical charge called a space charge. Since acrylic is an excellent dielectric, the injectedelectrons cannot escape. They accumulate under continued irradiation, forming a plane of negativespace charge inside the specimen. By carefully changing the orientation of the specimens and passingthem through the beam in two or more passes, or by rotating them as they are irradiated, complex3-dimensional space charge regions can be produced.

As the space charge grows, the resulting electrical field also increases. Eventually, the immenseelectrical stress overcomes the dielectric strength of the acrylic, and some of the chemical bonds that holdthe acrylic molecules together are ripped apart. This strips away additional free electrons (a processcalled ionization). These newly-freed electrons are also accelerated by the electric field, ionizing even

more acrylic molecules, and creating additional free electrons in a runaway process. Within billionths ofa second, electrically conductive channels form within the acrylic as the material suddenlyundergoes dielectric breakdown. As breakdown occurs, the previously trapped charge suddenly rushesout, accompanied by a loud bang(!), and thousands of electrically conductive branches feed current intoa main "lightning bolt" that exits the acrylic with a brilliant flash. Although pictures of the discharge seemto suggest that we are injecting high voltage into the block, in reality we are removing the high voltagecharge that was previously trapped within the block. The dielectric breakdown process occurs withinan incredibly short amount of time. For example, the electrical discharge within a 2 inch squarespecimens may only last for less than 60 billionths of a second! The following image shows a 4 inchsquare specimen as it was being discharged:

(Photo courtesy of Theodore Gray)

The miniature lightning bolts leave their fingerprints in the acrylic, forming a complex, branching,and permanent "lightning fossil" within. The current within the electrical discharge is typically hundreds,or even thousands, of amperes. The hot plasma within the discharge causes the acrylic to melt andfracture along each path, and higher current "roots" may even char the acrylic slightly. The exit point ofthe discharge appears as a small crater on the surface of the acrylic. The discharge point is typically locatedat a surface defect, or where a point of external mechanical stress has weakened the dielectric. Thedefect concentrates the electric field, creating a weak link where the breakdown process can begin.Although we inject a huge amount of negative charge into our specimens, the electrical breakdown

process actually originates from points which are more electrically positive (versus the space charge), soour Captured Lightning sculptures are actually "positive" Lichtenberg figures!

Actual discharge current measurements... and a paradoxDuring our 2007 production run, we were able to capture the shape of the current waveform as wedischarged a number of 4" x 4" x 3/4" specimens (similar to the specimen above). A special holdingfixture with copper foil plates made physical contact with the large surfaces of the charged acrylic
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specimen. A heavily insulated wire connected the pair of foil plates to a sharp tool which was usedto discharge the specimen. This wire was also passed through the center of an Ion Physics 50 kAwideband current transformer (CT). The CT transformed the discharge current pulse that flowed throughthe wire into a voltage pulse that could be captured and stored within a high speed Tektronix digitalstorage oscilloscope. The digitized waveform data was subsequently analyzed using an Excel spreadsheetin order to recreate the following waveform.

We found that, for 4" x 4" specimens, the discharge lasted for only 120 billionths of a second. Forthe specimen shown below, the peak current was almost 600 amperes, and consisted of four discretecurrent peaks. Other specimens showed between three and seven peaks. This suggests that the electricaltrees may have propagated via a series of advancing waves, where each current peak reflected a surgeof newly conducting channels ("streamers" and "leaders"). New channels apparently blasted their way

into previously untapped reservoirs of charge within the acrylic, briefly paused, then surged again, etc.The average discharge velocity was between 8.5 x 105 and 1.3 x 106 meters/second (526 and 790miles/second, or around 0.3% the speed of light). However, pauses between successive current surgessuggest that the peak discharge velocity during growth phases was significantly faster. Surprisingly,the average velocity within the specimen was actually 10-100 times faster than the velocity of

positive lightning leaders in air. This is thought to be due to the extremely high electrical field (estimated tobe ~10-20 million volts/cm) at the tips of the propagating discharges within the acrylic.

However, the high streamer velocity creates a paradox, since it is over 800 times the speed of soundwithin PMMA. This is inconsistent with Griffith's theory of crack propagation within solids, which

predicts that the maximum crack propagation speed within a solid is limited to the Rayleigh speed (i.e.,the speed of sound) or 1.614 km/second for PMMA. The current waveform clearly demonstrates thatthe chains of cracks and gas channels developed at a speed that was almost three orders of magnitudefaster than it should be from classical materials theory. We suspect that that potential energy (from theintense internal electrical field) causes "electronic breakdown" of the PMMA, generating a "detonationwave" of microcracks that propagates through the charge layer at hypersonic speed. This is an area ripefor future research. A Russian researcher, Yu N Vershinin, has termed the process of energy exchange betweenthe electrical field and propagating fractures as "electronic detonation". Not surprisingly, the discharge processalso generates a powerful shockwave (a loud BANG!), and a brilliant, miniature, blue-white "lightning" flash.

After the main discharge, there are often hundreds of smaller secondary electrical discharges as smallpockets of stranded charge redistribute themselves within the specimen. Larger figures often sparkleand sizzle for tens of seconds afterwards, making a sound similar to frying bacon, and intermittentsparking has been observed up to 30 minutes later. These smaller discharges often sting our fingerswhen partially discharged specimens are handled. Click on the following image to see some highresolution video taken during our November, 2007 production run showing primary andsecondary discharges.
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(Photo and video courtesy of Mike Walker and Theodore Gray)

Click on the Above image to see a video clip

of many Lichtenberg figures being discharged

Video clip of a huge 18" Lichtenberg figure being created:Following is another video clip of an 18" x 18" x 1" specimen being discharged during our 2005

production run. Before discharging, the estimated potential of the internal charge plane was 2.2 millionvolts. Because of it's size, this specimen had considerably more stored electrostatic energy, and thedischarge was quite loud and extremely bright! The actual discharge, although very brief, saturated thevideo camera image sensor. A multitude of secondary discharges can also be observed after themain discharge. (Video courtesy of Terry Blake. Specimen was owned, and discharged, by Jeff Larson.)

The rounded, crystalline flakes that make up the Lichtenberg Figure are actually chains of tinyconchoidal fractures. These shell-shaped fractures are characteristic of the way noncrystalline(amorphous) materials fracture when stressed beyond their breaking point. Since these tiny fracturesreflect light like tiny mirrors, illuminating the figures through the edges causes the entire figure toglow brilliantly with the reflected color(s) of the external light source.

Lichtenberg figures are fractalsLichtenberg figures exhibit branching patterns which tend to look similar at various scales ofmagnification. This self-similar property suggests that Lichtenberg figures can be modeled using a branchof mathematics called Fractal Geometry. Self similarity is a key property of fractals. Our LichtenbergFigures show a range of fractal patterns depending upon the magnitude of charge injected into the acrylic
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and how and when the specimens is discharged. Branching figures are technically called "dendritic"or "arborescent" (tree-like). If a large amount of electrical charge is injected into the specimens and it isthen immediately discharged, a very dense dendritic discharge is created, such as the leftmost figure

below. These dense discharges are quite similar in appearance to ferns or moss agate. If the level of chargeis reduced and the specimen manually discharged, a more classical, lightning-like or tree-like dischargeresults as the center example below. If premature breakdown occurs as we are actively irradiating aspecimen, tangled "chaotic" discharges occur. Some specimens show fascinating and complexcombinations of these basic patterns.

(Click for larger image)

Densely Dendritic Discharges(higher charge density)


Dendritic Discharges(lower charge density)


Chaotic Discharges(prematurely dischargedwhile being irradiated)

Self similarity can easily be seen in the following sequence of zooms from a 12" x 12" LichtenbergFigure with nominal dendritic discharges. The branches become finer and hairlike, ultimatelydisappearing. Similar fractal patterns are seen in aerial views of some rivers and their tributaries,

branching tree limbs, and the arteries, veins, and capillaries within your body.

It has recently been discovered that Lichtenberg figures can be modeled using a process called"Diffusion Limited Aggregation" or DLA. A useful macroscopic model that combines an electric fieldwith DLA is called the Dielectric Breakdown Model or DBM. The dielectric breakdown model appearsto describe the branching growth that characterize the dielectric breakdown process within solids, liquids,and gases.

Solarization, fluorescence, and birefringence:During irradiation, the acrylic glows a brilliant blue-white color. Although radiation chemistry studiessuggest that this may be a combination ofluminescence orCherenkov radiation, the reason(s) are notfully understood. You may also notice that our specimens have a discharge-free zone along all of theoutside edges. This is because acrylic is not a perfect insulator, so some of the internal charge "leaks away"

to the outside surfaces. This reduces the amount of stored charge along the perimeter to the point wherethe electrical field is no longer sufficient to break down the acrylic.

You may also notice that a portion of the acrylic has an amber tint - this is called solarization. Solarizationis thought to be caused by the formation of structural changes and defects through electron collisions,high energy x-rays, and the temporary trapping of ionic charges within the molecular structure of thePMMA. Solarization usually occurs within the region between the surface that was irradiated by theelectron beam and the discharge layer. During irradiation, electrons are initially traveling at about 99% ofthe speed of light. As they penetrate the specimen, they collide with acrylic molecules, rapidly coming toa stop within a fraction of an inch. The electrons in the beam have a tremendous amount of kinetic energy,and as they suddenly brake to a stop, they release this energy in the form of heat and very powerfulX-radiation. As the acrylic absorbs electrons and x-rays, various physical and chemical reactions occurthat may alter its physical and optical properties. Although the specific causes of solarization are notfully understood, there is evidence that irradiation creates unstable, or longer-lived "metastable",

compounds that preferentially absorb light at the blue end of the spectrum (250 - 400 nm). This causes
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some or all of the clear PMMA to turn green, brown, or amber.Some electrons may become trappedfor months, perhaps years, afterwards, creating color centers which may also contribute to the solarization.

Many irradiated specimens initially turn a bright lime green color which, over a period of minutes tohours, fades to amber. The solarized region may take months, or even years, to fade away. Fading can

be accelerated by gently heating the block in the presence of oxygen, or by leaving the specimen insunlight for an extended period of time. As oxygen diffuses into the PMMA from the outside andthe discharge layer, it bleaches the solarized region, causing the solarized layer to gradually becomethinner and thinner, eventually disappearing altogether. Most older Lichtenberg figures becomecompletely bleached. Although they no longer show any solarization, some specimens may showslight residual "fogging" from irradiation damage. Some specimens exhibit little initial solarization, while

a small number of specimens appear to permanently retain their amber color. Curiously, it has been foundthat fully charged specimens will retain their green color for many days when kept at dry icetemperatures. These specimens then change to amber after being discharged. There are clearlyseveral different processes that are associated with solarization.

Recently, it has also been discovered that the solarization layer may sometimes be fluorescent. Anamateur scientist from New Zealand, Daniel Rutter, discovered that monochromatic light from a greenlaser pointerchanges colorwhen passed through the solarized layer of a Lichtenberg figure. More recently,we discovered that the light from a near-ultraviolet source (such as a Blu-ray laser or even bright blueLED's) sometimes causes the solarized region to glow with a brilliant yellow-green fluorescence. Thisoccurs on some specimens but not others, and as the solarization fades over time, so does themysterious fluorescence.

Most specimens also exhibit slight changes in refractive index near the Lichtenberg discharge region.These behavioral differences are thought to be due to variations in the acrylic blends used byvarious manufacturers, permanent irradiation-induced changes to the polymeric structure of the acrylic,and residual mechanical stresses near the discharge fractures. Residual stresses near the Lichtenbergfigures can easily be seen as multicolored regions near the discharge plane when a sculpture is illuminated

by polarized light and then viewed through a second polarizing filter. When physically stressed,PMMA exhibits a property calledbirefringence. When viewed through polarizing filters, stress-induced birefringence causes changes in color that are related to the amount and distribution ofotherwise hidden stresses within the PMMA.

Natural Lichtenberg figures - fulgurites and lightning dischargesOccasionally, nature also creates "fossilized lightning". Called fulgurites, these are hollow andsometimes branching tubes that are formed when the powerful electrical current from a lightning strikecreates underground discharge channels within poorly conducting sandy or sandy-clay soils. Thesehollow channels were formed as the intensely hot channel from the lightning arc fused surrounding sand

and soil particles which then cooled to form a solid glassy tube. Some fulgurites also exhibitfractal characteristics as they split into smaller diameter root-like branches at further distances from the siteof the main strike.

Lichtenberg figures, sometimes called "lightning flowers" or "skin feathering", are sometimes formedbeneath the skin of unfortunate humans who have been struck by lightning. The victim will often have oneor more reddish radiating feathery patterns that branch outward from the entry and exit points of the strike:
http://www.accessscience.com/abstract.aspx?id=149500&referURL=http%3a%2f%2fwww.accessscience.com%2fcontent.aspx%3fid%3d149500http://en.wikipedia.org/wiki/Fluorescencehttp://dansdata.blogsome.com/2007/12/03/lichtenbergia/http://www.olympusmicro.com/primer/lightandcolor/birefringence.htmlhttp://www.usfcam.usf.edu/CAM/exhibitions/1998_12_McCollum/supplemental_didactics/04.Fulgurites.pdfhttp://en.wikipedia.org/wiki/Electric_archttp://en.wikipedia.org/wiki/Electric_archttp://www.usfcam.usf.edu/CAM/exhibitions/1998_12_McCollum/supplemental_didactics/04.Fulgurites.pdfhttp://www.olympusmicro.com/primer/lightandcolor/birefringence.htmlhttp://dansdata.blogsome.com/2007/12/03/lichtenbergia/http://en.wikipedia.org/wiki/Fluorescencehttp://www.accessscience.com/abstract.aspx?id=149500&referURL=http%3a%2f%2fwww.accessscience.com%2fcontent.aspx%3fid%3d149500


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(From "Lichtenberg Figures Due to a Lightning Strike" by Yves Domart, MD, and Emmanuel Garet, MD,

New England Journal of Medicine, Volume 343:1536, November 23, 2000

Medical terms for this phenomenon include arborescent lightning burn, arborescent erythema,keraunographic markings or simply ferning patterns. Although the exact causes are subject to somedebate, they appear to be the result of damage to small capillaries under the skin, perhaps caused by theflow of electrical current from the stroke, or by shock wave bruising from external flashovers just abovethe skin. The arborescent (tree-like) reddish marks fade away over a period of hours or days. Theyare recognized by forensic pathologists as clear evidence that a victim has been struck by lightning.The patient above survived with no permanent injuries, and the lightning flowers completely faded withintwo days. A small Lichtenberg figure has also been observed at the entry point where a high voltagespark penetrated the skin of an unfortunate (but surviving) local electrical experimenter who tookan accidental "hit" from a homemade 60,000 volt Marx Generator.

A similar phenomenon is sometimes seen when lightning hits a grassy field, as in this picture wherelightning struck a flagpole, leaving this beautiful 25 foot Lichtenberg figure on the green of a golf course:

(From "Lightning and Lichtenberg Figures" by Cherington, Olson and Yarnell, Injury, Volume 34, Issue 5, May 2003)

Note how similar the above figure appears to the Lichtenberg figure within this specimen (lit from belowby blue LED's):
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High voltage discharges to the surface of water can also create Lichtenberg figures. Some verybeautiful examples of both positive and negative Lichtenberg figures on water surfaces can be seen onDr. Colin Pounder's Lichtenberg figures web site.

Natural lightning sometimes creates transient "Lichtenberg Figures" in the sky. Air is an excellentdielectric and, although the physical breakdown mechanisms for air and PMMA are considerably different,the appearance of the branching discharges is quite similar. So it should not be surprising that the

branching forms of natural lightning also have fractal characteristics. This similarity can clearly beobserved during "anvil crawler" and horizontal "spider lightning". Spider lightning follows a thin,

positively charged cloud layer, and the slowly propagating discharges can crawl across the sky for 30-40

miles - literally spanning from horizon to horizon. On a much smaller scale, transient Lichtenbergfigures (often mistakenly called St. Elmo's Fire) often appear on the outer surface of cockpit windowsof airplanes as they fly within thunderstorms.

Similar branching fractal patterns also occur when thunderstorms generate electrically conductive leadersthat propagate downward from a charged cloud to the ground below. When one of these leaders connectswith an unfortunate object on the ground, a high current surge (called the return stroke) rushes backupward through the completed path, resulting in Cloud-to-Ground (CG) lightning strike.Exceptional examples of downward propagating positive leaders have been captured by SouthDakota lightning researcher, Tom Warner. Using high speed video imaging equipment, he was able tocapture the downward progression of leaders and the return stroke from apositive lightning bolt.Positive lightning is a significantly rarer (and considerably more dangerous!) form of lightning thannegative lightning. The "slow motion" video (below) shows the air breaking down, formingglowing conductive plasma paths (called leaders) that fan downward from a huge reserve of positive

charge within the cloud above. The brightly glowing tips of the positive leaders smoothly propagate,unlike negative leaders which propagate in a series of discrete jumps (called stepped leaders). Thefirst descending leader to finally connect with the Earth below completes the circuit, resulting in a

powerful Positive Cloud-to-Ground (+CG) lightning discharge.

The video clip below was captured at 7200 frames/second (FPS), and the actual elapsed time for the clipwas only a little longer than three thousandths of a second. The speed of the propagating leaders was

between 3 x 104 and 6.5 x 105 meters/second. This clip even contains a single frame which capturesthe beginning of the return stroke from the Earth going back up one of the leader channels. Even atthe majestic scale of natural lightning, you can clearly see similarities between the collection of

branching leaders and Lichtenberg Figures. Positive lightning also has a very long lasting "tail" offollow-through current which typically lasts for several hundred milliseconds after the initial strike connectsto ground. The combination of long propagation distance (often many miles from the main storm), veryhigh current (up to 300,000 amperes), and long follow-through current make positive lightning
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exceptionally dangerous. It tends to set fire or kill anything, or anyone, unfortunate enough to be in itspath. More of Tom Warner's fascinating videos can be seen on his page on YouTube.

Lichtenberg Figures can also be seen at some high energy pulsed power facilities, where deionized wateris sometimes used as a dielectric to briefly store large amounts of electrical energy. The famous photo

below is from Sandia National Laboratory's mighty Z Machine, the world's largest pulse generator. After

the completion of a high energy experiment, the water breaks down from the huge electrical stress,becoming an electrical conductor that safely dissipates unwanted residual energy from the system.The filamentary breakdown paths form Lichtenberg figures that dance across the water's surface. If youlook closely, you'll notice that many of the radial paths actually trace out high voltage electrical fieldlines along the surface of the water. Although impressive, this display is only dissipating "left over"energy, representing only a very small fraction (perhaps 5%) of the energy that was actually used duringthe previous pulsed power experiment.

(Click for a higher resolution 840 x 554 pixel image, 561 kB)

Holding a Lichtenberg Figure is about the closest you can come to holding fossilized lightning in your hand- Captured Lightning is indeed an accurate description. Most of the Lichtenberg figures shown on ourweb site were produced by irradiating various acrylic shapes using a 5 MeV Continuous Wave (CW)research LINAC - a 150 kW high power electron beam accelerator called a Dynamitron. A few werecreated using pulsed linear accelerators at significantly higher beam energies (10 - 15 MeV).Lichtenberg figures are completely safe - they have been electrically discharged and have noresidual radioactivity or X-radiation. And, as with snowflakes, every Lichtenberg Figure is a one-of-akind treasure.

Following are a pair 3-D images that can be rotated 360 degrees so that you can fully enjoy the beauty of

our doubly-irradiated Lichtenberg figures. The irradiation process results in very complex discharges
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within and between the two charge layers. Please wait for the images to completely download, then dragyour mouse to rotate the images for a full 360 degree view. (Warning: you'll need a high speedInternet connection to view these since they are each ~6 MB files and will take quite some time to fully load.)

3D Rotatable Image3D Rotatable Image

"Heavy Weather"(Courtesy of Theodore Gray)

"Windblown Lightning"(Courtesy of Theodore Gray)

Very few people have actually seen or held one of these rare objects, and far fewer have had the opportunityto own one. Stoneridge Engineering is proud to be the world's most experienced provider for these

beautiful and rare treasures. We offer a wide selection of 2D and 3D figures ranging in size from affordable

2 inch specimens through museum quality figures as large as 24 inches by 36 inches. Please visit ourgalleries to see the world's most beautiful Lichtenberg figures:Gallery 1 Gallery 2 Special Eye Candy Page

Everyone is a genius at least once a year.

The real geniuses simply have their bright ideas closer together.G.C. Lichtenberg

Thunder is good; thunder is impressive. But it is the

lightning that does the work.- Mark Twain

References and Further Reading:1. Gross, Bernard, "Irradiation Effects in Plexiglas", Journal of Polymer Science, Volume 27, 1958, Issue 115, Pages 135 - 1432. Hashishes. Yuzo, "Two Hundred Years of Lichtenberg Figures", Journal of Electrostatics, Volume 6, Issue 1 , February 1979, Pages 1-133. Chadwick, K. H., "The Effect of Light Exposure on the Optical Density of Irradiated Clear Polymethylmethacrylate", 1972 Phys. Med. Biol.17, Pages 88-934. Chadwick, K. H., and Leenhouts, H. P., "Fading of radiation-induced optical density in polymethylmethacrylate on oxygen diffusion",Phys. Med. Biol. 15 No 4 (October 1970), Pages 743-7445. L. Niemeyer, L. Pietronero*, and H. J. Wiesmann, "Fractal Dimension of Dielectric Breakdown", Phys. Rev. Lett. 52, 10331036 (1984)6. Gardner, Donald G., et. al., "Radiation-induced changes in the index of refraction, density, and dielectric constant of poly(methylmethacrylate)", Journal of Applied Polymer Science, Volume 11, Issue 7, July 1967, Pages 1065-10787. Akishin, A.A.; Tseplyaev, L.I., "Edge effect in radiation-charge dielectric materials", Physics and Chemistry of Materials Treatment, v 31, n1, Jan.-Feb. 1997, p 30-1. A similar paper is also contained within the book "Effects of Space Conditions on Materials", Akishin, A. I., NovaScience Publishers, 2001, ISBN 15903302858. Fothergill, J.C.; Dissado, L.A.; Sweeney, P.J.J., "A discharge-avalanche theory for the propagation of electrical trees. A physical basis fortheir voltage dependence", Dielectrics and Electrical Insulation, IEEE Transactions on, Volume 1, Issue 3 , June 1994, Pages 474 - 4869. R. A. Galloway, T. F. Lisanti and M. R. Cleland, "A new 5 MeV 300 kW Dynamitron for radiation processing", Radiation Physicsand Chemistry, Volume 71, Issues 1-2, September-October 2004, Pages 551-55310. Sessler, G.M.. "Charge distribution and transport in polymers", Dielectrics and Electrical Insulation, IEEE Transactions on, Volume 4 , Issue5 , Oct. 1997Pages 614 - 62811. Karczmarczuk, Jerzy, "Dendrites in Nature and in Computer", Foton 84/SPECIAL ISSUE, Spring 2006

12. C. M. Foust, General Electric Review: Instruments for Lightning Measurements (Includes Klydonograph and Lichtenberg Figures)

13. Watson, Alan and Dow, Julian, "Emission Processes Accompanying Megavolt Electron Irradiation of Dielectrics", Journal of AppliedPhysics, December 1968, Volume 39, Issue 13, pp. 5935-594014. Fujimori, S., "Fractal properties of breakdowns", Properties and Applications of Dielectric Materials, 1988. Proceedings., SecondInternational Conference on Properties and Applications of , 12-16 Sept. 1988, Pages:519 - 522 vol.215. Domart, Yves, M. D., Garet, Emmanuel, M.D., "Lichtenberg Figures Due to a Lightning Strike", New England Journal of Medicine,Volume 343:1536, November 23, 2000, Number 21, Images in Clinical Medicine16. H. Hiraoka, "Radiation Chemistry of Poly(methacrylates)", Radiation Chemistry, March 1977

17. Brown, R. G., "Time and Temperature Dependence of Irradiation Effects in Solid Dielectrics", Journal of Applied Physics, September1967, Volume 38, Issue 10, pp. 3904-390718. Yu. S. Deev, M. S. Kruglyi, V. K. Lyapidevskii and V. I. Serenkov, "Mechanism underlying the formation of dendritic or tree-like channels ina dielectric irradiated with charged particles", Atomic Energy, Volume 29, Number 4, October, 197019. Ebert, Ute and Arrayas, Manuel, "Pattern Formation in Electric Discharges", p. 270 - 282 in: Coherent Structures in Complex Systems, eds.:

D. Reguera et al., Lecture Notes in Physics 567 (Springer, Berlin 2001)

20. Yu.N. Vershinin, S.V. Barakhvostov, "Electron Processes in the Pulse Breakdown of Solid Dielectrics", 3rd International Conference

on Technical and Physical Problems in Power Engineering, (TPE-2006), May 29-31, 2006 - Gazi University, Ankara, Turkey (detonation
http://205.243.100.155/frames/interesting.htmlhttp://205.243.100.155/frames/interesting3.htmlhttp://205.243.100.155/frames/SpecialLichs.htmlhttp://205.243.100.155/frames/SpecialLichs.htmlhttp://www.if.uj.edu.pl/Foton/92-special%20issue/pdf/09%20dendryty.pdfhttp://www.eeel.nist.gov/817/pubs/spd-anthology/files/Foust%201931.pdfhttp://www.research.ibm.com/journal/rd/212/ibmrd2102E.pdfhttp://homepages.cwi.nl/~ebert/sit.pdfhttp://homepages.cwi.nl/~ebert/sit.pdfhttp://homepages.cwi.nl/~ebert/sit.pdfhttp://www.science.az/physics/lab29/pdf_tpe_2006/eem/c73.pdfhttp://www.science.az/physics/lab29/pdf_tpe_2006/eem/c73.pdfhttp://www.science.az/physics/lab29/pdf_tpe_2006/eem/c73.pdfhttp://www.science.az/physics/lab29/pdf_tpe_2006/eem/c73.pdfhttp://www.science.az/physics/lab29/pdf_tpe_2006/eem/c73.pdfhttp://www.science.az/physics/lab29/pdf_tpe_2006/eem/c73.pdfhttp://www.science.az/physics/lab29/pdf_tpe_2006/eem/c73.pdfhttp://www.science.az/physics/lab29/pdf_tpe_2006/eem/c73.pdfhttp://homepages.cwi.nl/~ebert/sit.pdfhttp://homepages.cwi.nl/~ebert/sit.pdfhttp://www.research.ibm.com/journal/rd/212/ibmrd2102E.pdfhttp://www.eeel.nist.gov/817/pubs/spd-anthology/files/Foust%201931.pdfhttp://www.if.uj.edu.pl/Foton/92-special%20issue/pdf/09%20dendryty.pdfhttp://205.243.100.155/frames/SpecialLichs.htmlhttp://205.243.100.155/frames/interesting3.htmlhttp://205.243.100.155/frames/interesting.htmlhttp://theodoregray.com/PeriodicTable/Samples/Electrons.2/index.qtvr.htmlhttp://theodoregray.com/PeriodicTable/Samples/Electrons.3/index.qtvr.html


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theory of high field breakdown in solid dielectrics)21. Vershinin, Yu. N., "Parameters of Electronic Detonation in Solid Dielectrics", Technical Physics, Vol. 47, No. 12, 2002, pp. 15241528. Translated from Zhurnal Tekhnichesko Fiziki, Vol. 72, No. 12, 2002, pp. 3943, ISSN: 1063784222. Theodore Gray, "Theo Gray's Mad Science: Experiments You Can Do At Home - But Probably Shouldn't", Black Dog & Leventhal

Publishers, 2009, ISBN 978-1579127916

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Lichtenberg Figures - Lightning as Art