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Meticulously researched and compiled, this poster functions as a thought-provoking guide to the astonishingly complex Mandelbrot set.
Meticulously researched and compiled, this poster functions as a thought-provoking guide to the astonishingly complex Mandelbrot set.
Meticulously researched and compiled, this poster functions as a thought-provoking guide to the astonishingly complex Mandelbrot set.
931 backers pledged $35,599 to help bring this project to life.

About this project

Mandelmap poster: a vintage style map of the Mandelbrot set project video thumbnail
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Mandelmap poster: a vintage style map of the Mandelbrot set

$35,599

931

UPDATE May 13 — 750 Backer Stretch Goal reached! Posters will now be shipped by fulfillment center! See updates page for more information.

UPDATE April 25 — $15K Stretch Goal Reached! Now both sizes of the poster will be printed with offset lithography!

Introducing the Mandelmap poster - a detailed map of the Mandelbrot set in a beautiful vintage style.

Overview of project 

I've been interested in fractals ever since I saw an article about them as a kid. I grew up excelling at math and appreciated fractals from that point of view. At some point later in my life, my inner emotions pushed me in the opposite direction to become an artist - eventually giving me an even deeper appreciation for fractals, which in turn gave me a renewed appetite for the science and math behind them. I have now put my two strengths together to create a poster that is both technically informative and aesthetically beautiful.

Fractals are a new class of geometry that I believe will continue to revolutionize the way humans think for centuries to come. Benoit Mandelbrot is sometimes called the father of fractal geometry and the most famous of all fractals is the one that bears his name - the Mandelbrot set.

The map's cartouche, displaying the simple equation
The map's cartouche, displaying the simple equation

Arising from a very simple and compact formula, the Mandelbrot set is stunning when seen as a whole... but its true wonders appear when you try to look closer at the border. I have been exploring the Mandelbrot set for several years, using many different programs and even coding my own explorer. A couple years ago, I started using patterns from the Mandelbrot set in my artwork (see some examples here: billtavis.tumblr.com/tagged/mandelbrot). I would usually just wander around and see what I could find, but at some point I realized I wanted to be able to know where I was going when I started zooming in. I found numerous guides on the net, and while each guide had some good tidbits, I was having trouble finding anything comprehensive. I wanted to put together everything I found into one big map that I could print and hang on my wall, but I very quickly realized that this was going to be a huge undertaking — so I decided I might as well take it to the next level and make it into an awesome poster that was not just for me but for everyone else as well! After nearly a year and a half of research, planning, and execution, the map is finally ready to go to print. 

That's where you come in! To distribute the poster widely, I will need to get an offset printing run, and that's where the majority of the funds raised will go. The rest of the funds will go to the large size digital prints, and the cardboard mailing tubes and shipping fees.

The inspiration for the map was to help an intrepid fractal explorer develop a strong intuition for where they are going when they zoom in on this amazing shape. By the end, it also became a fairly* comprehensive general overview of the subject. The text is written in a way that is accessible for people who have never heard of fractals, but even veteran fractalists might find something new here. Carefully compiled, I hope the poster inspires artists, mathematicians, scientists, and all the rest of you to think about fractals and our world in a new way. Its vintage style will look great in any home, office, or classroom.

*The poster could never cover everything since the Mandelbrot set is, literally, infinite.

Seahorse Valley illustration
Seahorse Valley illustration

About the poster

One of Benoit Mandelbrot's earliest publications about fractals, in 1967, was titled "How Long is the Coast of Britain?" Although he wouldn't actually coin the term fractal for another 8 years, the basic idea is there: the closer you look at the coastline, the more detail you see. So it seemed natural to treat the Mandelbrot set as if it were a large island surrounded by an ocean.

The Mandelmap poster includes:

  • Several familiar locations labeled with their colloquial names, together with accompanying illustrations. Find the Dragon Valley, and see why it's named that way.
  • Hundreds of bulbs labeled according to period numbers. Count to infinity by even numbers, count to infinity by odd numbers, or even find the Fibonacci sequence! It's all there in the period numbering.
  • Hundreds of external angles labeled according to how far around the set you are in a counter-clockwise direction. This maps the border of the Mandelbrot set to a circle.
  • Equipotential lines that show how fast points outside the Mandelbrot set escape to infinity under iteration of the equation.
  • Several high-quality zoomed-in renderings, with detailed information describing how to find similar locations.
  • Julia Medallions, and where to find them. The medallions correspond to Julia sets, which are very closely related fractals that use the same equation but in a slightly different way.
  • A clear and practical description for how to use the formula that defines the Mandelbrot set.
  • ... and much, much more!
The compass rose (origin)
The compass rose (origin)

Technical details and shout-outs 

All of the fractal renderings were created with software I coded myself using the CImg library. A good portion of the coding was done specifically for this project - this allowed me to get exactly what I needed at the highest possible quality. The map also includes several hand-drawn illustrations by Lena Martin. The text was rendered with Blender, and all of the assets were compiled into a final image using Krita. The wording on the map was copy-edited by Linda Andrews. There's a lot of great information out there on the internet, and while I could never list all the resources I used, the ones that stand out are Fractal Forums, claude, Wolf Jung, Miquel, and Bob Devaney.  Thank you!

Rewards

Anyone who pledges will have their name listed as a supporter on www.mandelmap.com as my way of showing thanks.

Anyone who pledges will also receive a postcard of the Mandelmap in the mail, with a handwritten thank you note. Please keep in mind that most of text is legible only on the poster-sized prints.

The rest of the rewards consist of various quantities of posters, available in two sizes. 

The standard size map is 36x24 inches at a full 300dpi for crisp details. That's 77 megapixels! It will be printed on high-quality 100lb paper with a matte aqueous coating. The standard-size poster will be printed with offset lithography. It's expensive to do a run, so funding this is the primary reason for the Kickstarter campaign.

Standard size mock up, photo by hobvias sudoneighm
Standard size mock up, photo by hobvias sudoneighm

For those of you who want something a step above, I am offering a huge 54x36 inch poster, w̶h̶i̶c̶h̶ ̶i̶s̶ ̶d̶i̶g̶i̶t̶a̶l̶l̶y̶ ̶p̶r̶i̶n̶t̶e̶d̶  UPDATE April 25 the $15K stretch goal was reached, so the massive size will now also be offset printed on 100lb paper with a matte aqueous coating!  I have already ordered a test print for myself, and it is awesome, the details look great at this size!

Massive size mock up, photo by hobvias sudoneighm
Massive size mock up, photo by hobvias sudoneighm

Thank you all for reading! Please share this project with your friends, family, and co-workers and help me make this poster a reality. There are social media links near the top of the page.

Risks and challenges

The biggest challenge by far was creating the poster, which is done. So at this point, the biggest risk is making the fundraising goal, and the biggest challenge will be shipping out all the posters at the end of the campaign - but I am confident that I can make it happen!

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Support this project

  1. Select this reward

    Pledge $7 or more About $7

    Thanks for the support! Get a postcard of the Mandelmap mailed to you, with a handwritten thank you. Your name will be listed as a supporter on mandelmap.com
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    Pledge $20 or more About $20

    EARLY BIRD special - pledge now and save! Be among the first to get one 36"x24" Mandelmap poster mailed to you in a shipping tube. These will be signed and numbered and mailed out first. You will also receive a thank you postcard in the mail and your name will be listed as a supporter on mandelmap.com
    Free shipping in the US

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    Reward no longer available 50 backers
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  3. Select this reward

    Pledge $26 or more About $26

    Get one 36"x24" Mandelmap poster mailed to you in a shipping tube. You will also receive a thank you postcard in the mail and your name will be listed as a supporter on mandelmap.com
    Free shipping in the US

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    677 backers
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  4. Select this reward

    Pledge $52 or more About $52

    Share the poster with your friends! Get three 36"x24" Mandelmap posters mailed to you in a shipping tube. You will also receive a thank you postcard in the mail and your name will be listed as a supporter on mandelmap.com
    Free shipping in the US

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    92 backers
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  5. Reward no longer available

    Pledge $68 or more About $68

    EARLY BIRD special - pledge now and save! Be among the first to get a massive size poster! These will be signed and numbered and mailed out first. Get one 54"x36" Mandelmap poster mailed to you in a shipping tube. You will also receive a thank you postcard in the mail and your name will be listed as a supporter on mandelmap.com
    Free shipping in the US

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    Reward no longer available 10 backers
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  6. Select this reward

    Pledge $80 or more About $80

    Massive size! Get one 54"x36" Mandelmap poster mailed to you in a shipping tube. You will also receive a thank you postcard in the mail and your name will be listed as a supporter on mandelmap.com
    Free shipping in the US

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    64 backers
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  7. Select this reward

    Pledge $145 or more About $145

    Distributor level. Keep one for yourself and give away or sell the rest! Get ten 36"x24" Mandelmap posters mailed to you in shipping tubes. You will also receive a thank you postcard in the mail and your name will be listed as a supporter on mandelmap.com
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    2 backers
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  8. Select this reward

    Pledge $160 or more About $160

    Share the massive size with your friends! Get three 54"x36" Mandelmap posters mailed to you in a shipping tube. You will also receive a thank you postcard in the mail and your name will be listed as a supporter on mandelmap.com
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    11 backers
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  9. Select this reward

    Pledge $260 or more About $260

    Distributor pack, the ultimate collection! Get three massive 54"x36" and ten standard 36"x24" Mandelmap posters mailed to you in shipping tubes. You will also receive a thank you postcard in the mail and your name will be listed as a supporter on mandelmap.com
    Free shipping in the US

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Funding period

- (30 days)