In principle, all the sunflowers in the world show a number of spirals that are within the Fibonacci Sequence. Coincidentally a number that is within the Fibonacci Sequence -)Īnd we have more examples in the two upper panels, cyan and orange, they are also arranged following values that are within the sequence: 34 and 21 spirals. Well, if you look at one of the typologies, for example the one in green, and you go to the illustration above right you can check that there is a certain number of spirals like this, specifically 55 spirals. In the top left picture we have highlighted three of the spirals typologies that could be found on almost any sunflower. Look at the following images of a sunflower:īy observing closely the seeds configuration you will see how appears a kind of spiral patterns. We have always said: nature is wise :-)ĪNOTHER CURIOSITY: Do you remember we had commented that there had a deep connection between the Fibonacci Sequence and Golden Ratio? Well, next we have another meeting point between both concepts. This leads to the characteristic structure in which all seeds are arranged into a sunflower, which is as compact as possible. …and so on, seed after seed, we will obtain gradually a kind of distributions like the ones you have in the following figures. Add a third ocher seed and make the previous traveling to the center, to stay side by side with the first one.Add a second green color seed and make the previous traveling to the center.And we find in many works created by the mankind in art and architecture, from the Babylonian and Assyrian civilizations to our days, passing through ancient Greece or the Renaissance. The result of this ratio (ie the division of a by b) is an irrational number known as Phi -not to be confused with Pi- and an approximate value of 1.61803399…įormerly was not conceived as a true “unit” but as a simple relationship of proportionality between two segments. It fulfills this ratio, also known as the Golden Ratio or Divine Proportion: the ratio of the sum of the quantities (a+b) to the larger quantity (a) is equal to the ratio of the larger quantity (a) to the smaller one (b). This is very special rectangle known since ancient times. See the complete process on the following series of illustrations: We start from a simple square to get that and use a classic method that requires only a ruler and drawing compass. It introduces the concept of Golden Ratio by constructing a Golden Rectangle. Once it has appeared the Nautilus we advance to the second part of the animation. Or you could explain in a more “genteel” way, saying that I have taken an artistic license □ Therefore I must confess that I did a kind of cheat with this animation. The truth is that this is something I discovered when I had completely finished the screenplay for this project and I was too lazy to change. It’s funny because if you perform this search at Google Images: “ spiral + nautilus” you will see how many images suggest that this shell is really based on the construction system described above.īut this isn’t correct, as it’s outlined below, on the “Making of” section. IMPORTANT NOTE: while watching the animation conveys the idea that the Fibonacci spiral (or the Golden Spiral, it doesn’t matter) is on the origin of the shape of a Nautilus, this isn’t absolutely right. It’s something similar to what happens when we try to approach to an ellipse by drawing an oval using circular segments: the result is not the same as a true ellipse. I have introduced a small optical correction in the animation in order to get the resulting curve more like a true Golden Spiral (more harmonious and balanced), as explained on this plate. Then we draw a quarter circle arc (90°) within each little square and we can easily see how it builds step by step the Fibonacci Spiral, looking at right graphic. And they are arranged in the way how we see in the diagram at left. We will create first a few squares that correspond to each value on the sequence: 1×1 – 1×1 – 2×2 – 3×3 – 5×5 – 8×8, etc. This is the next thing to be shown on the animation, appearing just after the first values on the succession: the process of building one of these spirals.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |