# How to Draw the Golden Spiral: 2 Easy Tutorials

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And finally, I would like to thank Ryan Butler, Auckland University of Technology, for his help with photography to document this experiment. In other situations, the ratio exists because that particular growth pattern evolved as the most effective. In plants, this may mean maximum exposure for light-hungry leaves or maximized seed arrangement.

There is nothing more glorious than seeing those young ferns unfurl in early spring. Often called a fiddle fern because of the resemblance to a violin scroll, there are so many fern types to see. The puzzle, per the authors, is how these gene regulatory networks that initially evolved to produce flowers were able to change so drastically. So, co-author Eugenio Azpeitia golden spiral in nature and several colleagues combined in vivo experiments with 3D computational modeling of plant development to study the molecular underpinnings of how buds form in cauliflower (both edible cauliflower and the Romanesco variant). The golden spiral ratio is a ratio that is derived from nature itself. We can say that nature is the original discoverer of this ratio.

According to the authors of this latest paper, the spiral phyllotaxis of cauliflower is unusual because those spirals are conspicuously visible at several different size scales, particularly in the Romanesco variety. The whole process depends on those branched tips, or meristems, which are made up of undifferentiated cells that divide and develop into other organs arranged in a spiral pattern. In the case of cauliflower, these cells produce buds that would normally bloom into flowers. Those buds develop into stems instead, but unlike normal stems, they are able to grow without leaves and thereby produce even more buds that turn into stems instead of flowers. Fractal geometry is the mathematical offspring of chaos theory; a fractal is the pattern left behind in the wave of chaotic activity. That single geometric pattern repeats thousands of times at different magnifications (self-similarity).

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We create a compelling visual brand and messaging platform by focusing on your buyers and communicating your unique solutions to their problems. We operate at the intersection of brand and growth marketing to empower companies with buyer-centric strategies that drive revenue. Although few of us ever see it, the inner ear is spiral shaped and the DNA cell structure is a double helix. The Pineapple demonstrates the same pattern as the pinecone we painted.

We believe that these findings will lead to many more advances in understanding skin dynamics and indeed the changes that occur in tissue when confronted by stretch. In our experiment, skin tracings of the advancing front (i.e. the non-sutured skin tension line that becomes deformed into curves under the force of rapid expansion) were marked out as detailed above (“Fig 1”). To the naked eye, we could see that we had achieved some degree of displacement of the original straight-line markings into curves (“Fig 2”).

Slow expansion over hours, days or weeks did not result in creating enough ‘shear’ in pigskin to produce spirals. Pigskin has three separate fat layers, separated by two layers of fascia [19]. The uppermost layer of fat in pigskin corresponds to the dermis in human skin—and authors have coined the term ‘intradermal adipocytes’ to describe these cells, as the term accurately reflects both their developmental origin and anatomical location [20]. Therefore, for the purposes of this experiment, the author decided to see if the causation of shearing forces between the uppermost two layers of pigskin (the epidermis and fatty dermis) would result in the formation of spirals along an advancing front. Romanesco broccoli (which, despite its name, is a hybrid between broccoli and cauliflower) grows in a golden spiral, a pattern based on the golden ratio. The spiral gets wider by a factor of φ for every quarter turn it makes.

## The Golden Spiral Symbol in Modern Times

And the distribution of strawberry seeds will follow a similar pattern. Spirals in Nature occur in many forms, but for us to find them, it is helpful to think of just 2 concepts. Another superstition is that this ratio shows the portion of the Parthenon. Since it is a mathematical term hence, it is very obvious that there must be a symbol to denote it. Hope the quick glimpse of the information included here has increased your curiosity to know every detail of this beauty.

Now, a team of French scientists from the CNRS has identified the underlying mechanism that gives rise to this unusual pattern, according to a new paper published in Science. Before one can study skin bio-dynamics or surgical closure techniques, one needs a good understanding of the directions of skin tension lines of normal skin. It is quite amazing that the Fibonacci number patterns occur so frequently in nature

( flowers, shells, plants, leaves, to name a few) that this phenomenon appears to be one of the principal “laws of nature”. Fibonacci sequences appear in biological settings, in two consecutive Fibonacci numbers, such as branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone. In addition, numerous claims of Fibonacci numbers or golden sections in nature are found in popular sources, e.g. relating to the breeding of rabbits, the spirals of shells, and the curve of waves The Fibonacci numbers are also found in the family tree of honeybees. From hurricanes to flowers and pinecones, spiral patterns are abundant in nature.

## Spirals in my Food

This is why the number of spirals in the centers of sunflowers, and in the centers of flowers in general, correspond to a Fibonacci number. Moreover, generally the petals of flowers are formed at the extremity of one of the families of spiral. This then is also why the number of petals corresponds on average to a Fibonacci number. Of course, this is not the most efficient way of filling space. In fact, if the angle between the appearance of each seed is a portion of a turn which corresponds to a simple fraction, 1/3, 1/4, 3/4, 2/5, 3/7, etc (that is a simple rational number), one always obtains a series of straight lines. If one wants to avoid this rectilinear pattern, it is necessary to choose a portion of the circle which is an irrational number (or a nonsimple fraction).

The Romanesco takes us on a journey into spiral fractals and if you slice a mushroom through the centre you can sometimes see a cross section of a curly spiral under the cup, sometimes referred to as the vortex. (just on UK is a good idea) Whelks and Periwinkles, Top shells, Limpets. There are so many variations to be found of just these types which you will see clearly how a spiral is the home of the mollusc that created it. If yes, then I am hundred percent sure that you must be confused between spiral ratio and Fibonacci sequence. Nowadays people have tattoos of this spiral curve on their bodies. You can see many things in nature that look quite similar to the above curve.

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Some plants express the Fibonacci sequence in their growth points, the places where tree branches form or split. One trunk grows until it produces a branch, resulting in two growth points. The main trunk then produces another branch, resulting in three growth points.

Even today, the golden ratio is in human-made objects all around us. Look at almost any Christian cross; the ratio of the vertical part to the horizontal is the golden ratio. To find a golden rectangle, you need to look no further than the credit cards in your wallet.

Pine cones, also called strobili, are woody, scaly fruits that dangle off evergreens and serve as the trees’ seed-bearing organs. You have no doubt noticed the satisfying spiral of their scales, which reflect the seeds they protect. They close tightly when it’s damp or cold, then open when it’s optimal for seeds to spread in the wind.

- According to experts, the golden rectangle should be framed at the base of the steps approaching the Parthenon, not at the base of its columns—as commonly shown in several illustrations.
- The snowflake could continue on like this for an eternity, growing the size of Earth itself, if it weren’t to stop accumulating moisture and, eventually, melt away.
- In geometry, a golden spiral is a logarithmic spiral whose growth factor b is related to j, the golden ratio.

Given the painter’s prior usage, it wouldn’t be unexpected for him to use it on the said painting as well. Just keep in mind that not every Da Vinci’s painting has clear evidence of the incorporation of the golden ratio and the golden spiral, so it’s difficult to conclude that all his masterpieces are based on them. Birds of prey are known to descend in a spiral movement as they home in on their prey, because of needing to always keep the prey in sight. There are spiral galaxies in outer space we still know so little about. Air flows in spirals around objects and water will form in a vortex spiral down your plug hole. Waves on the seashore are spirals that ever surfer knows how to read.

## Flowers and Branches

You can actually see the Fibonacci sequence in action in some natural spirals. In visual art like painting and photography, the golden ratio is used in composition because it is considered aesthetically pleasing. The universe may be chaotic and unpredictable, but it’s also a highly organized physical realm bound by the laws of mathematics.

- The results are presented here—the composite image created by overlaying all our tracings show a clear logarithmic spiral pattern, in our case very close to a golden spiral pattern seen in nature.
- In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller.
- There is nothing more glorious than seeing those young ferns unfurl in early spring.
- It is quite amazing that the Fibonacci number patterns occur so frequently in nature

( flowers, shells, plants, leaves, to name a few) that this phenomenon appears to be one of the principal “laws of nature”. - The end result is those fractal-like forms at several different size scales.
- It’s a natural example of the logarithmic or equiangular spiral.

1.Every spiral found in the earth follows the golden spiral rule. But this is not true because many spirals do not follow the same rule. Later, Leonardo da Vinci painted Mona Lisa’s face to fit perfectly into a golden rectangle, and structured the rest of the painting around similar rectangles. In order to optimize the filling, it is necessary to choose the most irrational number there is, that is to say, the one the least well approximated by a fraction. (It is obtained by multiplying the non-whole part of the golden mean by 360 degrees and, since one obtains an angle greater than 180 degrees, by taking its complement). With this angle, one obtains the optimal filling, that is, the same spacing between all the seeds (figure 3).

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For example, if the angle is 90 degrees, that is 1/4 of a turn, the result after several generations is that represented by figure 1. I would like to thank Jan Gardner at Auckland University’s Advanced Clinical Skills Centre for helping obtain pigskin and use of the Centre’s facilities for my experiments. This paper resulted from a study that forms part of my Ph. D research project at the University of Queensland’s School of Medicine and I would like to acknowledge my supervisor, Assoc.