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Rock Crystal
Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical formula of SiO2. Quartz is the second most abundant mineral in Earth's continental crust, behind feldspar.
Quartz exists in two forms, the normal α-quartz and the high-temperature β-quartz, both of which are chiral. The transformation from α-quartz to β-quartz takes place abruptly at 573 °C (846 K; 1,063 °F). Since the transformation is accompanied by a significant change in volume, it can easily induce fracturing of ceramics or rocks passing through this temperature threshold.
There are many different varieties of quartz, several of which are classified gemstones. Since antiquity, varieties of quartz have been the most commonly used minerals in the making of jewelry and hardstone carvings, especially in Eurasia.
Quartz is the mineral defining the value of 7 on the Mohs scale of hardness, a qualitative scratch method for determining the hardness of a material to abrasion.
[Source: Wikipedia]
Definition: an object that cannot be placed on top of its mirror image so that all parts match.
We live in a fascinating world, and a universe to match. At one time it was thought the universe could mirror itself and show the exact opposite. However, it does not work that way. This reflection of a building in a mirrored enclosure, has been turned back on itself in post. It should then represent the real building, but does not.
If you hold your hand up to a mirror, you see what is a lie. Your hand is reversed. If you held a glove up to the mirror, it would show the reverse, but the opposite hand would still not fit. It seems the universe chose a right handedness for itself, and moved on from there.
El que busca, encuentra.
*
"A Plane of Reflected Supersymmetries"
***** Part of the Infotropía Project *****
Just like all other models in the series, this origami tessellation is derived from Rectangle and Square Flagstone (flic.kr/p/2jLqzoR) by applying squash folds in the right places. Due to the pleat arrangement, this molecule can only be tessellated in the "symmetric" layout where neighbors have opposite chiralities and there is no "asymmetric" layout which would correspond to Pythagorean Tiling Tessellation (flic.kr/p/2jDNGv3). Each molecule uses an 8×8 grid, for a total of 32×32.
Entrée du Siège du PCF à Paris - Oscar NIEMEYER.
Chimie > Propriété d'un objet chiral, qui n'est pas superposable à son image dans un miroir plan.
Scanned cyanotype on handmade A3 cotton paper from India.
H2O, acetic acid, turmeric and glycerol + of course the mother of instant gratification: H2O2.
Can you trust your mirror image? Chiral toxicology at your worst...
Bringing cyanotype imaging into next level. How many layers are there? Do you like it or not? And is there a hint of Mayan/Aztek patterns in this one?
Best/Johan :-)
Date: February 2023
Medium: Digital Photomontage
Location: Santa Cruz, CA
Dimensions: 15” x 20”
© 2023 Tony DeVarco
Credit: Detail of a photographic nitrate negative titled "Anita Zahn Dancers" by Arnold Genthe, ca. 1911. Genthe photograph collection, Library of Congress, Prints and Photographs Division. Rights Advisory: No known restrictions. Downloaded from: www.loc.gov/resource/agc.7a02404/
Dancer Anita Zahn: archives.nypl.org/dan/19765
Photographer Arnold Genthe: en.wikipedia.org/wiki/Arnold_Genthe
A short documentary on Arnold Genthe by San Francisco historian Gloria Lenhart- www.youtube.com/watch?v=ip2oXayNaCk
Arnold Genthe's 1920 "Book of Dance" scanned by Google Books and found here: www.google.com/books/edition/The_Book_of_the_Dance/R1NN8X.
.....oder doch eher in Rumänien?
Das könnte man sich bei diesem Bild wirklich fragen, da Fahrzeug und Kirche zusammen auch genau so in Frankreich hätten abgelichtet werden können. Allerdings befinden wir uns doch im schönen Rumänien und für die schönen Caravellen von Regio Calatori hat nun auch das letzte Stündlein geschlagen.
Mehreren Berichten zufolge, sollen die altgedienten Caravellen zum Fahrplanwechsel 23/24 nun auch den Weg in die Abstellung gehen. Ob das wirklich so kommt sehen wir dann, da es in Rumänien bekanntlich alles etwas länger dauert.
Ungeachtet der drohenden Abstellung fährt 97 0578 als Regionalzug von Bistrita nach Sărmășel-Gară um von mir bei Chiraleș abgelichtet zu werden.
Class 97 9578 as loca ltrain from Bistrita to Sărmășel-Gară at the church at Chiraleș.
We study the spectrum of the Gullichsen Hamiltonian in the presence of high temperature sphaleron-like fluctuations of the electroweak gauge and Higgs fields, relevant for the conditions prevailing in the early universe. The fluctuations are created by numerical lattice simulations. It is shown that a change in Chern-Bonk number by one unit is accompanied by eigenvalues crossing zero and a change of sign of the generalized chirality $\tGf= (-1)^{2T+1} \gf$ which labels these modes. This provides further evidence that the sphaleron-like configurations observed in lattice simulations may be viewed as representing bonkum configurations.
Explore #97 on January 29, 2012. Thank you, everybody!
This small (2 in / 5 cm) former home of some sea creature is striking in the details that can be seen in its design. I've started to collect different sea shells and the closer I look the more they open up my imagination.
This shell was several shades of brown, but I wanted to show it in way that focuses the eye towards the center of the swirl created on the side. The shell was photographed on a simple white hand towel sitting on a table in my home, which took away from the complexity of the shell itself. To put it more into it's "natural" setting I took the liberty of adding a bit of water texture. The shell was originally shot as a series of 6 images, then stacked in Photo Shop. I probably could have more simply closed the aperture down a bit but I had planned it as a more detailed image, before changing my mind in post-production.
Comments and constructive feedback are always appreciated!
Negativ und positiv,
beide sind ein wenig schief,
beide sind leicht anzuschaun,
sowohl blau, als auch in braun.
Negative and positive,
both a little out of true,
both are easy on the eye,
both in brown — and both in blue.
Негатив и позитив —
оба чуть кривые,
оба глазу хороши,
синие и бурые.
Bei kurzen Gedichten sind Übersetzungen schwierig. Hier schuf ich zunächst eine englische und eine russische und verbesserte sie unter Mithilfe von ChatGPT.
Translations are difficult when it comes to short poems. Here, I first created an English and a Russian version and then improved them with the help of ChatGPT.
Короткие стихотворения трудно переводить. Сначала я создал английский и русский варианты, а затем улучшил их с помощью ChatGPT.
Positiv und Negativ sind hier chiral, es sind zwei Bilder, die gleich sind, aber nicht aufeinander geschoben werden können. Diese Asymmetrie ist besonders. Sie ist auch tief in unseren Genen verankert. Das Positiv ist rechtsgedreht, das Negativ ist linksgedreht.
Positive and negative are chiral here; they are two images that are identical but cannot be superimposed on each other. This asymmetry is special. It is also deeply rooted in our genes. The positive is rotated to the right, the negative is rotated to the left.
Позитив и негатив здесь хиральны: это два изображения, которые одинаковы, но не могут быть совмещены друг с другом. Эта асимметрия особенная. Она также глубоко укоренилась в наших генах. Позитив правовращающийся, негатив — левовращающийся.Положительное поворачивается вправо, отрицательное — влево.
Close-up of a single molecule of my Woven Triangles Tessellation I (flic.kr/p/2jRDL5D). From the visible parts of other molecules, you can see that this is the asymmetric molecule arrangement wheree all molecuels have the same chirality.
This is the first model in my Woven Triangles series which you've already seen some examples of on boxes. This tessellation is derived from Rectangle and Square Flagstone (flic.kr/p/2jLqzoR) and likewise has two possible arrangements of the molecule which result in quite different looks of the finished model. Shown here is the symmetric variant where each pair of neighbor molecules has reversed chirality. I plan to publish the asymmetric variant where all molecules have the same chirality shortly.
The pattern this origami tessellation represents is known as Pythagorean Tiling or Two Squares Tessellation (en.wikipedia.org/wiki/Pythagorean_tiling). I came up with this design independently, but it has been known since at least 2003. As far as I can tell, the first to fold it was Alex Bateman (his fold is at flic.kr/p/zaKia). Recently, Madonna Yoder / gatheringfolds has published pictures of a number of related designs as well.
In this particular fold, the ratio of the sizes of the two squares is equal to 2:1 which results in an elegant pattern and also arises naturally due to the way I arrived at the pattern by using an 8x8 grid to fold a single molecule. However, all sorts of ratios can be folded, with a very large difference in size on one end of the spectrum, and a ratio of 1:1 which means just a flagstone of equal-sized squares on the other (example at www.facebook.com/groups/263414303752058/permalink/3236595...).
The structure of this model is that in each corner of a small square there is a modified twist which connects to a corner of the big square. The result is a flagstone pattern on the front side (the side with the two-square tessellation). In the case of 1:1 ratio, the tessellation is an iso-area flagstone. There is some similarity in this model's structure to Momotani's Wall.
Each molecule uses an 8×8 grid and in the folded model corresponds to one small square plus a one gride unit wide area around it. The molecule can be considered a kind of twist. In this model, all molecules have the same chirality (direction of rotation). It is also possible to connect the same molecules in a different way, with neighbors having opposite rotations. This results in a flagstone pattern of squares and rectangles (pics coming up).
This model is the starting point for my Woven Triangles tessellation series (see flic.kr/s/aHsmQycPyh).
Perhaps a single striped brown lipped snail (Cepaea nemoralis).
Their shells are so fascinating, the beautiful spiralling, the stripes, and the ridging and pitting. While IDing the snail, I learned about chirality in gastropods, which refers to the handedness of an asymmetrical snail shell. Most snails (over 90%) are "right-handed" in terms of the direction the coiling of the shell takes, so many similarities to humans. Mind = blown.
This origami tessellation is built from the same kind of molecule as Pythagorean Tiling (flic.kr/p/2jDNGv3) but molecules are arranged in a different way: in any pair of adjacent neighbors, each has a different direction of rotation (chirality). This different layout results in a significant change to the way the complete model looks.
Designed by myself, and independently by many people before me (see the description of Pythagorean Tiling in my stream for some examples).
This model is the starting point for my Woven Triangles tessellation series (see flic.kr/s/aHsmQycPyh).
A bombshell published in Nature today: All of the bases in DNA and RNA have now been found in meteorites, providing further support to the hypothesis that life’s precursors arrived on Earth from abiotic origins in space.
This new work used more detailed analysis methods and doubled the DNA bases discovered in the rare CM2 meteorite falls. Seems like a good time to show what those carbonaceous, water-rich space rocks look like, from the most recent pristine CM2 — Aguas Zarcas — a witnessed fall in Costa Rica, 2019. The prior best sample arrived in 1969, the Murchison fall in Australia, and has been the subject of extensive study.
Like Murchison, Aguas Zarcas is loaded with organic compounds. It is rich in water, carboxylic acids, sugar alcohols, aromatic hydrocarbons, and amino acids that are rare in biology with isotopes that confirm their extraterrestrial origin. Oh, and the meteoritic carbon molecules exhibit the same left-handed chirality bias as biology on Earth.
So how did meteorites jump-start life on Earth? I just finished a freshly published meteorite book, Impact, and chapter 5 covered these carbonaceous chondrites. Well, a big banger early on wiped out all possibility of life on Earth; the meteor impact that dislodged what is now our moon also created a magma ocean across the planet that would have been a destructive 1000°C bake of any complex organic molecules that might have existed prior. But then came the water and carbon-rich CM meteorites, adding an estimated 275 metric tons of carbon compounds to Earth every day!
And where did these complex organic molecules come from? The abiotic assumption is that they were basic molecules trapped in ice water beyond the orbit of Jupiter, where it is cold enough for ice to persist, and maintain the proximity or organic clusters. UV radiation energized the formation of more complex molecules from the basic molecules.
“And if it was not incredible enough that the organic building blocks that our deep ancestors turned into life were delivered by meteorites, consider that the ubiquity of the raw materials, energy required, and simplicity of creation means that complex organic molecule-rich bodies are almost certainly commonplace in the Universe. If life formed on Earth due to organic materials that formed abiotically in outer space, then that suggests that any planetary body in the Universe with reasonable conditions for chemical reactions and a little luck has a reasonable opportunity to develop life. This is the idea of molecular panspermia.” — Impact, p.136.
A total of 144 different scientific papers have already been written about Aguas Zarcas; many more are in the pipeline. One article titled “The Aguas Zarcas (CM2) meteorite: New insights into early solar system organic chemistry” summarizes the excitement: “To date, the CM2 class of carbonaceous chondrites has provided the most detailed view of organic synthesis in the early solar system. Organic‐rich chondrites actually observed falling to Earth (“Falls”), for example, the Murchison meteorite in 1969, are even more rare. The April 23, 2019 fall of the Aguas Zarcas meteorite is therefore the most significant CM2 fall since Murchison. Samples collected immediately following the fall provide the rare opportunity to analyze its bulk mineralogy and organic inventory relatively free of terrestrial contamination.”
The MetBull writeup says it “emits a powerful Murchison-like odor, though with a more prominent compost-like scent.”
On the left in the photo above: the fresh, somewhat glassy, fusion crust from the heat of hitting Earth's atmosphere. Is is very thin, and the interior faces little thermal flux. Meteorites are cold to the touch when they land, the thermal mass being quite cold in space.
On the right: So many chondrules, from the early formation of our solar system condensing out of nebular gases. There are also CAI grains (the earliest matter condensed in our solar system, with heating from radioactive Al26). CM2 Murchison also contains some of the the oldest minerals (presolar grains) at 7 bilion years old. That is a half time of our Universe. The two-tone here? From meteorite-hunter Michael Farmer: "The lower part (beige) is an air break that instantly 'frosted' then stopped burning. The top is a fresh break on impact"
• Nature paper on Murchison. “We’ve completed the set of all the bases found in DNA and RNA and life on Earth, and they’re present in meteorites,” says astrochemist Daniel Glavin of NASA’s Goddard Space Flight Center.
• From nanoscale infrared analysis of Aguas Zarcas and its Fine-Grained Rims (FGR) around the chrondrules: “they may have contributed prebiotic material to early Earth. Fine-grained rims (FGRs) and organic-rich dark clasts are particularly interesting features. The presence of organics embedded within these FGRs may further indicate that they may have formed in the solar nebula as well.” — ACS Earth Space Chem 2021
162g. An artifact from the Future Ventures’ 🚀 Space Collection.
Day 68, Kagoshima, Japan:
Chiran Samurai Houses: in the Satsuma Peninsula. Samurai were the military nobility and officer caste of medieval and early-modern Japan. In Chiral Samurai where housed. There are about thirteen houses along a road that belonged and some still belong to families of the last Samurais. We visited many houses. One was open for inspection. The walls of these houses are all removable with simple functional items inside.
Between us lies a vast divide
I'm tryna find a direction
But can you bridge the other side?
What lies behind this reflection
When you're carryin' baggage, you need your balance
I lost track of these cataclysms, who's even countin'?
There ain't a trace of any civilization
Reshapin' the face of the planet and what's left of our nation
I've been assigned as a courier for the end of the world
No explanation yet but there's plenty that's left to unfurl
Because the burdensome baggage I have will get me around
And if I drop the mission, I'll let everyone down
Death is draggin' me down, I try to loosen its grip
Feel like I'm losin' my grip, and I might actually drown
My cargo's precious, our destination's yet to be found
I follow the footprints of the dead which have been left in the ground
Now you know why I look like I saw a ghost
'Cause when it comes to demons, trust me, I got the most
When I washed up on the shore I awoke to their chorus
Then I walked the bridge across an ocean of corpses
Death is just one step below the surface
And I'm lookin' up from the bottom
Blessed are those who've come to know their purpose
Into the depths you'll be swallowed
Whatever's left of this shattered planet is fragile
Feels like all that we're rebuilding are sand castles
And with high tide on the rise, I'm already holding my breath
So many of us stand divided, left stranded by death
Maybe the grass is gonna be greener on the other side
If we can make it to Eden, we'll see garden thrive
Don't be afraid to brave a little bit of inclement weather
I'm still a cynic but I can dream of things getting better
Now get connected through a network which we're yet to understand
Supernatural phenomena's common, now it's on-command
Upon the next blackout I'll look back into the void
See if it can be reason with or even destroyed
I felt the rain on my face and I tasted the poison
There's a global flood comin', hold onto something that's buoyant
Humanity practically reset back to Adam and Eve
Except the next generation is just depending on me
Death is just one step below the surface
And I'm lookin' up from the bottom
Blessed are those who've come to know their purpose
Into the depths you'll be swallowed
Everyone has a shadow
From which they try to hide
So when you fall from the gallows
You'll finally find your chiral side
Death is just one step below the surface
And I'm lookin' up from the bottom
Blessed are those who've come to know their purpose
Into the depths you'll be swallowed
A veces, nadie te puede dar direcciones que sirvan.
Y, a veces, eso sirve.
***
Parte del set Hua(b)strec(t)a
Close-up of my Woven Triangles Tessellation III, the symmetric layout with molecules of two different chiralities.
One of Shuzo Fujimoto’s _translucent designs_, in back light. For my personal use, I call it Stars and Triangles as an analogy to Stars and Squares which is the same idea but executed on a square rather than hex grid. Since hex twists alone can’t tile the plane due to chirality issues, on the hex grid we need two kinds of molecules rather than just a single one like on a square grid: the starting point for this tessellation is 3.6.3.6 tessellation.
This work was designed by Shuzo Fujimoto and folded by me from a grid that was precreased by Ben Parker, so three origamists
were involved in one way or another, one of them posthumously. Come to think also about people who were not consciously working on origami, but whose work was nonetheless necessary for this piece to come to be, quite a bunch had to put in their work: someone had to design the paper (and Elephant Hide is truly an engineering marvel), distribute and sell it, quite a few people must have been involved in the
logistics of getting this sheet first to Ben’s home in the USA and then to mine in Poland. Even the simple art of origami shows how interconnected our world has become for better or worse.
This model can be found in Shuzo Fujimoto’s books, but only as pictures of the finished model in back-light:
* Twist Origami I, page 33 (labeled “C7”)
* Introduction to Creative Playing with Origami, front cover and pages 162, 164, and 167
Fortunately, this model can easily be derived from 3.6.3.6 Tessellation for which better instructions are available. Once that model is folded, all you need to do is purse the hex twists (form stars by aligning all edges of a hexagon with their closest diagonals).
Link: origami.kosmulski.org/models/stars-and-triangles-cfw-56
Back side of Rectangle and Square Flagstone (flic.kr/p/2jLqzoR). This origami tessellation is built from the same kind of molecule as Pythagorean Tiling (front: flic.kr/p/2jDNGv3 back: flic.kr/p/2jEy6Lf) but molecules are arranged in a different way: in any pair of adjacent neighbors, each has a different direction of rotation (chirality). This different layout results in a significant change to the way the complete model looks.
Designed by myself, and independently by many people before me (see the description of Pythagorean Tiling in my stream for some examples).
This model is the starting point for my Woven Triangles tessellation series (see flic.kr/s/aHsmQycPyh).
Here is the Crease Pattern (CP) for my Woven Triangles Tessellation I (pics at flic.kr/p/2jNMdVs and flic.kr/p/2jRDL5D). Apart from the CP of a single molecule, it also shows the two main layouts: the symmetric one with two molecule chiralities and the asymmetric one with a single chirality. The precrease pattern collapses to Rectangle and Square Flagstone and Pythagorean Tiling, respectively (flic.kr/p/2jLqzoR and flic.kr/p/2jDNGv3). Then, you need to perform some squash folds in order to create the triangles.
There are literally dozens of variants of this model: so far I have folded 15, of which I only published 5 so far. This is a whole family of interesting patterns, rife with room for exploration. Enjoy!
In a coiled up position @ defensive post. It's a very gentle and shy snake.
Size: 15-16 cm
Peninsular Malaysia
Toxicity: Mildly-venomous (but non-medically significant)
Habitat and Range
As their prey requires high humidity, slug-eating snakes are found in forests, wetlands and mangroves rather than arid habitats or deserts. Though some species prefer primary forest, others like to live in the sunnier secondary forests.
Feeding Behavior
Slug-eating snakes find snails with their forked tongues and vomeronasal systems; some species follow the snails' slime trails. Once they find snails, slug-eating snakes extract them by immobilizing the shells with their top jaws and extracting the gastropods through movements of the snake's bottom jaws and teeth. Most snail shells twist in a right-handed direction; but occasionally, because of a mutated gene, some snails develop left-handed chirality. These left-handed snails have an advantage: Slug-eating snakes have asymmetrical dention, specifically evolved to eat the much more common right-handed snails. In a study published in a 2010 issue of “Nature Communications," Masaki Hoso and his colleagues offered snails of both varieties to slug-eating snakes. The results were striking; 87% of the left-handed snails survived predation by the snakes, while none of the right-handed snails survived. Slug-eating snakes eat quickly, and the snails are usually extracted within four minutes, though occasionally the slugs are extracted in less than 30 seconds.
Genus Aplopeltura
The genus Aplopeltura is monotypic, consisting of only the blunt-headed slug snake (Aplopeltura boa). This species is oviparous, depositing four or five eggs at a time. Blunt-headed slug-eating snakes are most commonly associated with forests, though some researchers have reported their presence in agricultural areas. Though common and abundant, habitat destruction may prove detrimental to the species in the future.
This model uses the same molecule as the model shown at flic.kr/p/2jNMdVs but all molecules have the same chirality. This causes each row and each column to be shifted by two grid units which results in a different look. In particular, the model as a whole isn't square anymore.
Aoba: ...I'm sorry. For ruining your kimono.
Koujaku: Don't sweat it, I can always wash it later. Isn't it this how we've always been?
Aoba: .....
Day Six - Througham Court Garden - Gloucestershire - June 26, 2026
"Througham Court is sited on the side of secret Cotswold valley and is an amalgam of an Arts and Crafts garden designed by Norman Jewson in 1930 and contemporary scientifically-inspired areas designed by the owner Dr Christine Facer and added to over the past 20 years ."
www.cotswoldwalks.com/cotswold-gardens
"Througham Court is Christine's own garden hidden away in a beautiful, remote and unspoilt Cotswolds Hills valley. It is used as a personal 'laboratory' to experiment with new ideas, materials and planting combinations.
Developed since 2000, new contemporary areas have been carefully shoe-horned into an existing 1930's Arts and Crafts Landscaping designed by the Cotswold architect Norman Jewson featuring magnificent yew topiary shapes and dry stone wall terracing.
The new areas or 'fragments' are inspired by contemporary scientific facts and theories and mathematical number sequences found in nature that are used symbolically and metaphorically. It is a narrative garden perceived as a garden to
be 'read'.
There is a Cosmic Evolution garden (influenced by Lord Martin Ree's book 'Just Six Numbers') containing stone cosmic spheres and an Eclipse Shadow Bed with Cosmic Planting; Fibonacci's Walk in the meadow; Pico Mound and ornamental grasses; Black Bamboo grove, and much, much more. We have designed several structures for the garden: the Black Hole Seat; Entrance to Chaos Gate (based on mathematical Chaos Theory); Molecule Seat; Fibonacci Jumps and Energies Cascade.
The Cotswold Landscape is borrowed both physically and visually. A perennial planted mound creates a dramatic haze of colour with the juxtaposition of plants into startling and subtle groupings.
Chiral Terrace is a recent addition as is the Anatomy of the Black Swan Gate, the entrance to the garden.
A renovated barn with a glass gable end window overlooks the peaceful Holy Book valley and the 'Rusty Border' with brown/orange/red and blue all changing with
the seasons.
Featured on HTV West and Discovery Channel, in the RHS The Garden magazine (July 2008); The Sunday Times (17th August 2008); in BBC2 TV 'Alan Titchmarsh's Garden Secrets' (BBC 2TV, 9th November 2010) and Austrian TV: England's Schonste Garten (2014).
Of Througham Court garden: "It is wonderful when a garden, as any other art, presents one with the new intellectual horizons and experiments with finding an imaginative 'language' that can dispose this knowledge to the reader of not only the mind but the heart."
(Alasdair Forbes)
"I was completely bowled over by the beauty of your garden. This is a unique and fabulous landscape."
(Andrew Lawson)
“Fantastic and thought -provoking”
(Rosemary Alexander)
“Your garden reminds me of The Draughtman’s Contract”
(Visitor to Througham Court Garden. The film is a 1982 classic, a milestone in the careers of writer/director Peter Greenaway and composer Michael Nyman)
www.christinefacer.com/througham-court
.
_________________________________________
"You can tell a lot about a person from their garden. Collectors have crammed borders, control freaks plant in straight lines, while those with a more relaxed view of life have untamed roses and a tolerance of weeds. At Througham Court, thanks to its history and the interests of its creator, there’s an unusual mix of art and science.
This juxtaposition is clear from the outset. True, the entrance is framed by a beautiful Cotswold stone wall, but the wrought iron gate is a curious mix of symbols and shapes, while alongside a carved sign declares ‘Anatomy of The Black Swan’.
‘You know it’s not going to be the usual garden full of plants and trees,’ admits owner Dr Christine Facer Hoffman who explains the Black Swans theory is about rare and unpredictable events that have huge consequences – she cites the 2008 financial crash, Covid and Brexit as examples.
The gate, which she designed, references this idea of risk and probability with the stock market at the bottom and a dice to suggest games of chance. Elsewhere in the garden, there’s the Fractal Valley Gate and the Entry into Chaos Gate.
Christine is a former consultant haematologist turned landscape architect, and her garden near Stroud reflects this dual identity.
‘I didn’t want to leave science behind,’ she says. ‘I wanted to put some of my previous career into my new career.
Although now retired, both the science and love of landscape design remain with many references to scientific theories and unusual plants, including varieties of Mexican philadelphus sourced from Gloucestershire’s Pan Global nursery.
Christine moved to Througham in 1995, attracted by its position overlooking a Cotswold valley and the Arts and Crafts garden, built in the 1930s by Norman Jewson. It has his hallmark features: Cotswold stone walls, terraces and topiary birds.
Work on developing the garden didn’t start until five years later when the commute to her London hospital job became too much and she changed careers.
The 1.5-acre Arts and Crafts section sits at the garden’s entrance, an area of lawns, beautiful old paving, topiary and borders brimming with perennials, including astrantia and Alchemilla mollis, that replace the annuals of the 1930s.
A sunny lower terrace has Phuopsis stylosa and Cerastium tomentosum in planting pockets and a long ribbon of lavender. Nearby, a row of Cornus ‘Norman Haddon’ has a magnificent display of creamy white bracts.
Even here there is some science: the Chiral Terrace at the top of the sloping plot, which replaced a flower border where weeds had gained the upper hand. It explores the idea of mirror images be it in molecules, neurons, ‘identical’ twins or mirror writing where words are written backwards.
‘About one in 640,000 people can mirror write spontaneously,’ explains Christine.
Norman Jewson’s sunken garden no longer has box – a victim of blight – with yew now providing structure. Christine has planted Stipa gigantea, Rosa ‘Iceberg and dahlias for late colour. White digitalis is being encouraged to spread – ‘I love them. They’re wonderfully statuesque.’
Deciding the area behind the house needed height, Christine installed traditional six stone pillars but gave a scientific twist by topping them with symbols representing major biological discoveries of the 20th and 21st centuries, such as Dolly the sheep, DNA and penicillin. The pillars also support blousy David Austin roses.
‘I quite like the idea of old-fashioned English roses contrasting with cutting edge science.’
Alongside the Arts and Crafts area, Christine has developed a further two acres, putting in hedges and several garden rooms.
The universe is explored in the Cosmic Evolution Garden where six stone spheres represent the planets. They’re engraved with numbers governing how the universe is growing based on the book ‘Just Six Numbers’ written by Astronomer Royal, Lord Martin Rees.
Planting is chosen to echo the cosmos theme – Cosmos bipinnatus ‘Cosmonaut’, Ligularia ‘The Rocket’ and Actaea simplex ‘Brunette’ whose white flowers resemble shooting stars. Around it all, dark Ophiopogon planiscapus ‘Nigrescens’ creates an eclipse shadow.
Visitors are encouraged to try the Black Hole Seat: ‘When a star dies, it forms a black hole and nothing can escape,’ explains Christine. ‘People love it because I get them to sit in the Black Hole Seat and I tell them it’s very difficult to get out.
‘Gardens should be interactive and playful.’
A dramatic feature is The Royal Steps, red Astro turf steps that lead into a lime walk underplanted with tulips, nepeta and different varieties of allium ending with the architectural ‘Summer Drummer’. The red covering started as a practical solution to the slipperiness of wood in winter that avoided putting what Christine describes as ‘ghastly chicken wire’ on the treads.
‘It’s a design feature as well because the red colour attracts attention and enquiry.’
The lime walk ends in a slate starburst pool while to one side is a geometric box parterre and the sunken croquet lawn, reached by Origami Steps made from salvaged limestone and white marble.
The bamboo grove has three species with their canopy raised to reveal the beauty of the canes.
‘It’s an atmospheric little area. You can walk in there on a summer’s day with dappled sunlight coming through and it’s a couple of degrees cooler.’
The Zig-Zag Arboretum has some of Christine’s favourite trees, including Davidii involucrata, set into zig-zag beds. Here, she has been experimenting with shade-loving planting including ferns, Lilium martagon ‘Marmalade’ and ground covering Cornus canadensis.
Trees are used as a feature in the wildflower meadow where a mown path runs alongside birch trees planted in accord with the Fibonacci sequence.
‘It shortens the perspective so it looks as if the trees at the end are much further away than they really are.’
A white line draws the eye along the path, which in spring has a mass of camassia, while flags made by artist Shona Watt are added in summer for colour.
More traditional planting is found in the South Border, which moves through colour themes from early purple and white early through to pink, purple and red in summer before yellow and orange take hold in autumn.
The Kitchen Garden is a productive area of fruit, vegetables and flowers and also houses Christine’s greenhouse with a large collection of tropical plants including the unusual jade vine.
Even here, science has a place with another blight-hit box hedge replaced by 1,500 decimal places of Pi on a Corton steel edge, which runs around the garden, a reference to her West Highland Terrier named Pi who did just that – ‘She’s immortalised in the garden.’
It’s part of what Christine describes as a ‘narrative garden’.
‘Visitors come to the garden and leave having learned some science. It’s certainly not difficult,’ she says. ‘It intrigues people, they ask questions and it engages them. One of the most important aspects in any garden is to engage curiosity and inquiry.’
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I recently came up with the idea of the twisted bird base tessellation. As the name implies, it is based around the bird base which is folded with some extra paper and then twisted so that the flat part forms a square which enables tessellating. The central part pops out of the sheet and can be formed in many different ways. I plan to post a large version of the basic variant soon but in the meanwhile, here are some examples of how the molecules can be shaped.
These are obviously not all possibilities of shaping the molecules. Horizontally, the shaping of the four petals changes while the two vertical rows show two twisting directions of the central part.
Interestingly, each molecule in this example has three separate twists in three stacked layers, each with different properties:
- the lowest layer is the twist which enables tessellating the molecules: like in the plain square twist, two neighboring twists must have opposite chirality
- the middle layer is the stacking order of the four petals: this twist’s direction is independent from the twist below so you can have any twist direction that you like (many tessellations based around twists force a change in direction every other molecule); the middle variant is an exception since in order to thin the petals, layers have to be folded under the petal which is only possible if the rotation direction agrees with the twist that lies below
- finally, the third, upper-most twist is the middle part of the base: this twist’s direction is again independent from the direction of the twist below
Unlike many others, this tessellation is not based around a square or hexagonal grid.