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This instructable demonstrates and explains blooms, a unique type of sculpture I invented that animates when spun while lit by a strobe light (or captured by a video camera with a very fast shutter speed).

Unlike a traditional 3D zoetrope, which is essentially a flip book of multiple objects, a bloom is a single coherent sculpture whose ability to be animated is intrinsic to its geometry.

What you are viewing in each of the above videos is a bloom spinning at 550 RPMs while being videotaped at 24 frames-per-second with a very fast shutter speed (1/4000 sec). The rotation speed is carefully synchronized to the camera's frame rate so that one frame of video is captured every time the bloom turns ~137.5º—the golden angle. Each petal on the bloom is placed at a unique distance from the top-center of the form. If you follow what appears to be a single petal as it works its way out and down the bloom, what you are actually seeing is all the petals on the bloom in the order of their respective distances from the top-center. Read on to learn more about how these blooms were made, why the golden angle is such an important angle, and how these are related to the Fibonacci numbers. You will also find some tips for constructing the turntable and strobe light required to animate blooms.

Blooms are available at Shapeways, a 3D printing service.

Step 1: How the Blooms Were Designed to Create This Effect

The placement of the appendages on blooms is critical to the success of the animation effect. The positions are based on a specific phyllotaxy (i.e. leaf order) used by nature in a number of botanical forms, including pinecones, pineapples, sunflowers, artichokes, palm trees, and many succulents.

The photo above shows just such a succulent. I have numbered the leaves from youngest to oldest. If you follow the numbers in sequence you will find that each leaf is approximately 137.5º around the core from the previous leaf. 137.5º is a very special angle, called the golden angle, based on the golden ratio. The golden ratio is such an important number in mathematics that it's been assigned to the greek letter α (phi). When the golden angle is used by nature as a growth strategy it leads to the formation of spiral patterns. If you were to count the number of spirals in these patterns you will find that they are always Fibonacci numbers (e.g. check out the spirals on these pinecones).

In designing the blooms, I used essentially the same method employed by nature. I placed the appendages one-at-a-time starting from the top-center, positioning each appendage 137.5º around the center from the previous appendage and also a little further out and/or down.

So when I animate these blooms by spinning them with a strobe light (or video camera) I am, in a sense, recreating the process that I used to make them in the first place. Below are two stop-motion animations of some of my earlier work with Fibonacci spirals. You may these helpful in gaining a better intuition about how this animation technique operates.

The first animation shows a self-similar tiling, in which every piece is a unique size, but all pieces are the same shape. In the video each piece is removed (and later added) at an angle of ~137.5 degrees from the previous. Note: this is not CGI (computer-generated imagery); it is a stop-motion animation of actual laser-cut pieces of MDF.

(BTW, if you would like to make one of these Fibonacci tilings for yourself, check out my instructable, which includes the cutting file.)

The second animation shows the TransTower, a sculpture based on the same geometry as the tiling above. The transformations in this tower result entirely from rotating the individual layers by the golden angle with respect to their neighboring layers. (Note: this is not CGI; it is a stop-motion animation of actual laser-cut MDF.)

<p>John, You were wondering about some other natural object to check out. Pine Cones spring to mind</p>
<p>Thanks for the suggestion! I would love to animate a pine cone, but I've had a hard time finding one where the scales are sufficiently regularly spaced, and/or the central axes are sufficiently straight. I've seen pictures of pine cones that would seem to fit the bill (like the two in the pic below), but I've never found an actual specimen. But I haven't given up!</p>
<p>Hi John,</p><p>Fantastic work! I thought you might be interested in seeing some F-Z's I made using blender. I used python to place the objects in a sphere shape, then spun the sphere and rendered each frame: </p><p>https://www.youtube.com/watch?v=ivM_fi4qOdI</p>
<p>Hi Mangakid,</p><p>I'm working with my son in Fusion 360. We are builiding a fibonacci bloom. Would you be open to sharing your python code with me. I'd like to use it as a tool to help him see how to program in Autodesk. </p>
<p>Nice work! Thanks for sharing it!</p><p>(If you wouldn't mind adding the word &quot;blooms&quot; to your title, I'd appreciate it, since I'm trying to get that to be the term people use in referring to these--as you can see by the current title of this instructable.)</p>
<p>Blooms, a beautiful name for them!</p>
<p>Thrilling journey to make these sculptures and the spinning platform!</p>
<p>Awesome, can I discuss this with you? Awesome lighting as well! hello@maxrichardson.com</p>
<p>Hello from NYC . they are awesome!! How do I get one? </p><p>This is art, just beautiful! M. </p>
<p>Thank you for your kind comments. I'm working with a manufacturer to make these available with the necessary turntable and strobe light. Stay tuned!</p>
<p>Hi John, love the work. I am buying a couple of your pieces. They give me pure joy! I wanted to potentially bring them to a party and put them on a vinyl player spinning at say 33 or 45 RPM. What would I need regarding a strobe for this to work? I wondered what the speed of the strobe would need to be if the speed of the turntable was reduced by say 10 times. How many times would the strobe need to fire per minute to create 'a 3D effect'. Thank you! My email is hello@maxrichardson.com</p>
Any estimated time frame? I would like to purchase as a bday gift
<p>Thank you very much, your work was a great inspiration!</p><p>This is my attempt:</p><p><iframe allowfullscreen="" frameborder="0" height="281" src="//www.youtube.com/embed/VT36s4eyMLo" width="500"></iframe></p>
<p>I was utterly mesmerised by those videos.</p><p>Thank you so much, I have just sat here chortling away merrily to myself just watching them over and over.</p><p>Elegant, beautiful, naturally inspiring. Genius in motion.</p>
<p>This is a project I've been waiting to do for a long time now that I just recovered! Would you be so kind as to share the stl files to me? I'll be showing them (with proper credit) on a 3d printing showcase in Tenerife. E-mail: balonmanoamorir@gmail.com</p>
<p>Thanks John for the files. It's not the best thing I've ever done, but it works, and it's cool to watch. I have a dc motor with a reducer, running at 32 rpm and a decent enough $8 ebay strobe. The video is from my ipad converted to gif and I took out all the black frames. It looks better in real life than on video. I'm trying the bloom next. </p>
<p>I have just received 2 sculptures (awesome looking), but haven't been able to locate turntable and strobe light info to get everything set up immediately.</p><p>Can you advise on what i need?</p>
<p>This instructable provides information on making the strobe and turntable. You will also need to write some simple code to control them with the Arduino micro-controller.</p>
I am fascinated. It reminds me of a pinecone. I seen the artichoke, i think the same would apply with a pinecone. I gotta give your idea a whirl!
<p>I love the fibonacci series. Thank you so much for this! I love the last video and see the shape being applied as a sky scrapper. </p>
<p>Yes, I have also thought that it might make an interesting building. Please tell me if you know somebody that wants to build it!</p>
<p>The first set of videos are mesmerizing too :)</p>
<p>I am well aware of Fibonacci spirals and their role in nature. I see them everywhere. This is all so cool.</p>
<p> that is insane Sooo beautiful</p>
<p>I've implemented the basic bloom sphere structure using Blender and a Sverchok scripted node. The basic codes and example are on <a href="https://github.com/elfnor/bloom_sphere" rel="nofollow">github</a>.</p><p>Explanations and some gifs are over at <a href="http://elfnor.com/bloom-spheres-in-sverchok.html" rel="nofollow">Look Think Make</a>. </p><p>Thanks for the inspiration.</p>
<p>Thanks for posting source code to play with!</p>
<p>Very coo! Thanks for sharing!</p>
<p>nice..</p>
<p>nice..</p>
<p>Hi John,</p><p>Are links to .stl still active in this Instructable? I noticed the DB link had been removed. You had sent the link to me personally about a year ago.Thank you. :)</p>
<p>Hello John, tell me how to get the file sizes of your shapes in STL format? </p><p>I want to make these for her concert in Russia. My mail aleksa-panov@yandex.ru</p>
<p>About the squealing sound of the motor using the ESC / BEC: the frequency of the signal, like a PWM signal does with a DC motor, causes the squealing. It might be difficult to really get rid of the squealing sound. An alternative is to control the speed using a potentiometer and a setup with an IR diode or a hall sensor to count and manage the RPM's according to the strobe frequency.</p>
or smooth the pwm'ed signal? A capacitor would do it wouldn't it?<br><br>
<p>Thanks! I'll look into that.</p>
<p>These are the most amazing thing i have seen yet...you sir are a total genius! </p>
<p>Mahalo for your examples of the sublime beauty of mathematics and the pleasure they bring! Your work makes me long for a 3D printer and a laser cutter.</p><p> A simple FET / microcontroller combination would switch the LED efficiently but the &quot;firing&quot; capacitor / charging network should be sized to the needed rep rate and pulse width. Enabling a watchdog timer is also good insurance to avoid leaving the LED on. Sync to the turntable with a sensor ( hall or optical ) would be easy. </p>
<p>You put a huge smile on my face today. Love the pieces. </p>
<p>Thanks! You put a smile on *my* face.</p>
<p>Majestic is all I can say about this sculpture.</p>
<p>please share your stl's pretty please?</p>
<p>You are a very talented,creative and generous artist.Have you considered doing something like this in a larger scale? Maybe a public installation. It's just the thing to inspire an interest in art, craft, science, and math. And of course technology and engineering.</p>
<p>Thank you for your kind words. There would be a number of technical challenges to overcome in order to make these substantially larger, but I'm hopeful that it will happen one day.</p>
<p>fantastic work! a file link would be greatly appreciated :) turnontunein at googlemail dot com. cheers! plan on illuminating with leds from the inside, if that works out :)</p>
<p>This is fantastic work</p>
Great work! You might want to check out the work of Johan Gielis on natural shapes and the superformula!
<p>Thanks, and Thanks for the reference! Very intriguing!</p>
<p>This is just awesome!</p>
<p>beautiful</p>

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