The Complex Geometry of Islamic Design

In Islamic culture, geometry is everywhere. You can find it in mosques, madrasas, palaces and private homes. This tradition began in the 8th century CE during the early history of Islam, when craftsman took preexisting motifs from Roman and Persian cultures and developed them into new forms of visual expression. 

This period of history was a golden age of Islamic culture, during which many achievements of previous civilizations were preserved and further developed, resulting in fundamental advancements in scientific study and mathematics. Accompanying this was an increasingly sophisticated use of abstraction and complex geometry in Islamic art, from intricate floral motifs adorning carpets and textiles, to patterns of tile work that seemed to repeat infinitely, inspiring wonder and contemplation of eternal order.

 Despite the remarkable complexity of these designs, they can be created with just a compass to draw circles and a ruler to make lines within them, and from these simple tools emerges a kaleidoscope multiplicity of patterns. So how does that work? Well, everything starts with a circle. The first major decision is how will you divide it up? Most patterns split the circle into four, five or six equal sections. And each division gives rise to distinctive patterns. 

There’s an easy way to determine whether any pattern is based on fourfold, fivefold, or sixfold symmetry. Most contain stars surrounded by petal shapes. Counting the number of rays on a starburst, or the number of petals around it, tells us what category the pattern falls into. A star with six rays, or surrounded by six petals, belongs in the sixfold category. One with eight petals is part of the fourfold category, and so on. 

There’s another secret ingredient in these designs: an underlying grid. Invisible, but essential to every pattern, the grid helps determine the scale of the composition before work begins, keeps the pattern accurate, and facilitates the invention of incredible new patterns. Let’s look at an example of how these elements come together. 

We’ll start with a circle within a square, and divide it into eight equal parts. We can then draw a pair of criss-crossing lines and overlay them with another two. These lines are called construction lines, and by choosing a set of their segments, we’ll form the basis of our repeating pattern. 

Many different designs are possible from the same construction lines just by picking different segments. And the full pattern finally emerges when we create a grid with many repetitions of this one tile in a process called tessellation.

By choosing a different set of construction lines, we might have created this any of the above patterns. The possibilities are virtually endless.  

We can follow the same steps to create sixfold patterns by drawing construction lines over a circle divided into six parts, and then tessellating it, we can make something like the above.

Here’s another sixfold pattern that has appeared across the centuries and all over the Islamic world, including Marrakesh, Agra, Konya and the Alhambra. 

Fourfold patterns fit in a square grid, and sixfold patterns in a hexagonal grid. 

Fivefold patterns, however, are more challenging to tessellate because pentagons don’t neatly fill a surface, so instead of just creating a pattern in a pentagon, other shapes have to be added to make something that is repeatable, resulting in patterns that may seem confoundingly complex, but are still relatively simple to create. 

This more than 1,000-year-old tradition has wielded basic geometry to produce works that are intricate, decorative and pleasing to the eye. And these craftsman prove just how much is possible with some artistic intuition, creativity, dedication along with a great compass and ruler.

The Winter That Froze Wine

The freeze had come literally overnight. On January 5th, temperatures plummeted. This was not a normal cold snap. The entire continent, from Russia to Italy to England, froze overnight. And the cold stayed. The Baltic Sea froze for four straight months. But the Adriatic Sea – between Italy and Greece – froze solid too. Ships that got stuck in the ice saw their whole crew starve and die before the ships were freed. In London, the “Great Frost” iced over the Thames. Almost all the rivers in the north and center of Europe froze, in fact.

Food became scarce quickly, not just due to animals freezing in their pens. Bread literally froze solid. Wine and beer, too. Only hard liquors such as vodka, whiskey, and rum remained liquid. There are stories about how wolves roamed freely in villages, looking for anything left to eat. And sometimes what they ate were the villagers who had simply frozen to death.

Keep reading



When Donald Trump was running for president, he talked a lot about putting people back to work. And one of the industries he focused on most was the coal industry. He even put on a hard hat and waved around a pick axe to show how much he loved coal.

But there simply aren’t very many coal jobs to be had any more in the U.S. That’s not because of anything Obama did. Coal jobs are decreasing because demand for coal is decreasing, and because machines now do much of the work.

In 1985 the coal industry employed a over 178,000 miners. By 2016, it employed just 56,000.

By contrast, in 2016, wind and solar energy provided more than 6 times the number of jobs as coal. The trend is toward even more jobs in wind and solar, regardless of what Trump does.

Solar energy is exploding worldwide, an almost sixfold increase in just the last 5 years.  But America ranks fifth in the production of solar energy, behind China, Germany, Japan and Italy.

If we really want to lead - if we really want to join the New Energy Economy - we have to go with the energy of the future, not the energy of the past. The other option — the one Donald Trump is proposing – leaves us following, not leading.

It’s our choice.

16th Century Book Can Be Read Six Different Ways

It’s not everyday you see a book that can be read in six completely different ways, and this small book from the National Library of Sweden is definitely an anomaly. According to Medieval book historian Erik Kwakkel, this 16th century text has a special sixfold dos-à-dos (or “back to back”) binding with strategically placed clasps that makes it possible for six books to be neatly bound into one. This particular book contains devotional texts, including Martin Luther’s Der kleine Catechismus, which was printed in German between the 1550’s and 1570’s.

While it could be hard to keep your place in this book, you can’t ignore that the engineering of it is quite a feat. In the age of the Kindle, Nook, and iPad, it’s a nice reminder of handcrafted ingenuity.

11 Rookie Boy Groups That Dance Perfectly In Sync


There are various reasons to stan your favorite boy groups, ranging from their amazing vocals to their dorky personalities. But above all, perfectly synchronized choreographies is one of the biggest factors that brings many fans into the fandom. These dances are what K-pop is known for, and for good reason; watching a group of attractive guys perform in 100 percent synchronization is an exhilarating experience!

These rookie boy groups debuted in 2016 or 2017 and are already on top of their synchronization games:


Anytime you’re feeling down, watching ASTRO dance will immediately get you in a good mood. Always full of energy, these six boys will make your level of happiness increase sixfold.

Some day the kindness you give out will come back to you. Maybe not as soon as you’d like, but it will be here. Threefold, sixfold, tenfold. Your life will be full of ‘thank you’. Full of ‘l’m so glad you’re alive while I am.’ Blossoms everywhere. Love raining down on you. It will come.


Life After The Feeder Tank

This is Shokin, and he is a fairly typically hibuna (common) goldfish. His name comes from the Japanse word 賞金 meaning prize; because that’s exactly what he was. A petstore in my area has a gumball machine, you put a quarter in and if a yellow gumball comes rolling down you get a fish out of the feeder tank. I just so happened to get a yellow gumball and out of the tank of overcrowded feeders I took home a skinny, pale, and underfed common. Shokin is my prize, but not because I won him, but rather because he has grown into such a beautiful fish. A bright and active fish many guests mistake him for a small koi when they visit the pond. Last June he weighed a petite 6g, and even through the harshest winter on record he’s managed to increase his weight sixfold.

Contrary to popular belief feeder fish are not inherently more sickly or less hardy, in fact it is quite the opposite. The fish that do survive being shipped in a bag with hundreds of other fish and then often kept in less than ideal water conditions are the strongest of the strong. Shokin arrived most likely on a tuesday in that store, packed in less than a gallon of water with 150 other feeders. I won him on a friday, so that means not only did he survive nearly a week in a feeder system but he managed to avoid being netted and sold as food. In may of last year he spawned with my calico ryukin Kai and his son Izoku (who you can see below) is not even a year old and already weighs as much as his father:

So this is a friendly reminder that while my main focus is fancy goldfish every goldfish keeper should be able to appreciate a common goldfish, and what many feeders go through only to end up as a meal. Just because a fish is free or bred to be food for another fish does not render it’s life worthless. Any fish when well cared for can turn into a lovely adult and goldfish have an amazing biological capacity to rebound from periods of severe neglect. On behalf of Shokin and all his feeder brethren that do not get a happy ending in a big pond, consider taking a feeder home with you if you have the space and resources.

The Gross body is physical body that is made up of the Panchmahabhutas – the five primordial elements, i.e., Akash (vacuum), Vayu (air), Agni (fire), Jal (water) and Prithvi (earth) and is subject to a sixfold change: birth, subsistence, growth, maturity, decay, and death. This is the dense physical body. Gross body is simply the vehicle of all the other Principles (bodies) during physical incarnation. Annamaya & part (physical manifestation) of Pranamaya Kosh reside in Gross (physical) body. Gross body needs gross food, drink and air which it gets from Annamaya and Pranamaya Kosha. At death the physical body perishes and its five constituent elements are dissolved.

The Subtle or the astral body (Linga Sharira) is where lives mind and intellect. Manomaya and Gyanamaya Kosh and part of pranamaya kosha resides in Astral or Subtle body. Linga Sharira contains pranamaya kosha, movement of the pranic force directing our physical and mental activities. This movement happens through nadis or channels, conductors of energy which are controlled by the six chakras. Vital sheath is a subtler sheath when compared to annamaya kosha. This is composed of vital energy. As long as this vital energy exists in the organisms, life continues. This sheath is responsible for our physiological functions namely breathing, digesting, metabolizing, circulation, endocrinal, neural, skeletal, muscular etc.

The Linga sharira (subtle body) surrounds the Sthula Sharira (physical body) as an aura of energy. The Nadis (subtle energy channels) exist in this subtle medium through a fine merger into the physical medium. This is the “vital body” and the prototype and reflection of the physical body. It comes into existence before the physical body as the latter is built and formed upon and around it and it only fully fades out and dies when the very last remaining particle of the deceased physical body disappears and disintegrates. In the internal astral body there are counterparts of organs outside. They are called astral senses. A yogi hears through astral ears and sees through astral eyes. Thus he can hear sounds from distant lands, he can see objects in distant localities. This is called clairvoyance and clairaudience.

When a person dies, his or her gross body (sthula sharira) is burnt. This being in fact the ‘Antya ishthi’ (antyeshthi) the last sacrifice offered in fire, but the soul cannot quit the gross body without a vehicle of some kind. This vehicle is the Linga-sharira or subtle body, sometimes described as angustha-matra (of the size of a thumb), invested in which the deceased person remains hovering near the burning ground or crematorium. It is the vehicle for and of Prana.

The Upanishadic texts reiterate the existence of a purusha (being) of the size of the thumb (angustha matram) enshrined in the interiors of the heart - “The self (purusha), that is of the size of a thumb (angustha), resides in the cave of the heart. The self who is the size of a thumb is a light (jyoti) without smoke.” This “being” dwelling inside the heart has been equated with the ‘jiva’ or the ‘self’ which carries the consciousness and a meta-physical body (prakriti), also termed as the karana sharira. Kathopanishad says “This shining, luminious angustha-matra entity residing in the cave of our heart is “vibhrajate because of which the whole world is illuminated.”

Astral Body’s Lower Mind: This sheath is the also energy of action. This mental sheath is composed of two qualities, mana (mind) and buddhi (intellect). Mana is the rational, linear, sequential, thoughtful mind. Buddhi is the quality of discrimination which comes after knowledge, after the removal or the absence of ignorance. The former constitutes the manomaya kosha, while the latter is called as the Vigyanmaya Kosha.

Astral Body’s Higher Mind: The Vijnanamaya kosha is the sheath of the intellect (buddhi) and intuitive knowledge/wisdom which gives us the discriminative capability that helps to differentiate between virtues & vice, good & bad, right and wrong, truth & untruth. It controls the mind, the senses, the fructifying samskaras & all activities of the body. The ego-driven intellect can lead to actions when it gets co-mingled with the memories and is clouded over by the manas which result in pain and suffering. Its knowledge is affected by the moods of the mind and other factors. Through the practices of meditation, regular self-study & enrichment of knowledge through libraries & discourses could lead towards devotion. Our mind becomes purified and the intellect can then begin to depend more and more on the pure intuitive wisdom rather than be influenced by the ego. As you begin to experience this aspect of existence, you discover that this sheath is merely an illusion covering over the eternal self. Hence the self is different from the body, unchanging, ever pure and free from modifications. Therefore, the self is a witness of the Vijnanamaya Kosha.

Anandmaya Kosh resides in The Causal body (Karana Sharira). Causal body needs bliss or peace which it gets from Anandmaya Kosh. Karana Sharira or Causal body is the map template which is the sole cause for the gross and subtle bodies in the future birth of the soul that is not liberated or detached from the causal body. Karana Sharira controls the formation and growth of the other two bodies, and determine every aspect of the next birth.

Karana Sharira is the doorway to the higher consciousness. It is associated with the state of dreamless sleep and samadhi. It links individual consciousness with the collective consciousness. Experiences (samskaras) from our past lives are stored in the causal body, it carries the information and knowledge acquired during the previous births. The attachment of Maya and intense desires for the worldly objects and pleasures, called “vasanas” also go along with Karana Sharira.

At the time of death, both the causal and astral bodies (that remain together) separate from the physical body. Once the soul is completely detached from its causal body it goes to the abode of God. The soul never needs to come back to the world again except for the God’s wish. When they come back to the world they come in the form of Gurus (Perfect masters). Guru is the one who leads the created to the creator. Guru is the descent of the Divine in human form to create the right conditions for the seekers to ascend to his Divine essence (Moksha or Enlightenment or Chaitanya).

(Sadgurus or Perfect masters are in reality, the seers who have realized the Absolute or have reached the highest realm of spiritual attainment, are present forever in the whole universe whether in an embodied or in an un-embodied state. They operate in gross, subtle, or mental world. They have been chosen to execute the Divine Mission and work together for the execution of the Divine Mission – Liberation of the seekers.)

#zx017 - Vanadinite
Fusion of: Perry (Imperial Topaz) and Brookite
Gem Type: Vanadinite
Weapon(s): Spear
Skills/Powers: A fusion of two gems with impeccable sense of direction, Vanadinite’s third eye grants them the ability to see all the possible paths to a destination and pick the fastest. They use hoverboards sixfold as wings, allowing them great mobility in the air and protection in battle.
Personality: Inherits Perry’s natural wisdom and calm, Brookite’s reflexes and ability to improvise, and the insatiable curiousity of both. Uses their ability to fly as a way to seek out information and expand their knowledge.

draw your oc in what you're wearing right now!!

doesn’t matter what you’re in–pjs, sports gear, nothing–stick ‘em on your competitor/npc!!

for extra special bonus points, draw yourself in their clothes*
*sizes may vary a shitload

Printed in the late 16th century book is an example of sixfold dos-à-dos binding, where six books are conjoined into a single publication but can be read individually with the help of six perfectly placed clasps. This particular book was printed in Germany and like almost all books at the time is a religious devotional text.