In a recent post, I discussed how looking at forests and fractals evokes a sense of awe.   The research studies found that natural fractal structures, like trees, and man-made fractals, like certain art, stimulates awe, altruism. It might be that looking at these structures that repeat patterns across very large and small scales evokes a sense of infinite. The abundance of the infinite might even support altruism, since giving any amount of the infinite still leaves one with the infinite.  When I see the same rich patterns in larger and larger (or smaller and smaller) scales, I feel a sense of infinity.  I have the same feeling when I participate in Thich Naht Hanh’s meditations on a tangerine. When we eat a tangerine, Thich explains, we can be aware of the sun, soil and people that nourished the tangerine. When we peel the tangerine, we can find a seeming infinity of sensations, smell and sight, if we peel mindfully. Eating the tangerine, slowly, we can find an infinity of sensations in our mouth as well as tastes. In these practices, I feel awareness of the very large and the very small, and feel a wonderful sense of abundance. It struck me that those enjoying coloring mandalas might feel something like this.

Mindfulness meditation gives me this rewarding feeling of abundance in the present. While, there is a huge amount of scientific literature on the positive effects of mindfulness practices (Farb, Anderson and Segal 2012), for me the reward is a fuller experience of life in the present moment. Similarly, I think that the coloring is its own reward. Nonetheless, I think it is helpful and interesting to know about the research on how coloring brings other rewards. Several studies randomly assigned people to various coloring activities and found that coloring resulted in significant mood improvement (Eaton and Tieber 2017, Babouchkina and Robbins 2015, Carsley, Heath and Fajnerova 2015, Van der Vennet and Serice 2012, Curry and Kasser 2005). Interestingly, these studies involved coloring in circles or mandalas. One study reports that the circle shape is important. People randomly assigned to color circle mandalas showed significantly greater mood improvement compared to those assigned to color within square shapes (Babouchkina and Robbins 2015). But after reading this I wondered if there are other aspects of the mandalas that might have an effect similar to fractals that research demonstrated to have such a positive effect on mood (as we reviewed in our post on math, pattern and awe).

Most mandalas I have seen are symmetrical, but they are not fractals. Fractals are symmetrical (or at least similar) across scales, large and small. But some spirals are fractals and also have an overall round shape like a mandala. So I wondered about spirals of the type seen throughout nature. These spirals are fractals because if we look at smaller and smaller scales, we see the same spiraling patterns.  I find the natural spirals found in a sunflower particularly fascinating, because we see many overlapping clockwise and counterclockwise spirals. It is quite hypnotic, and reveals a fascinating underlying dynamic. So we created a coloring book with these images.

Also, the hypnotic arrangement of seeds on a sunflower reveals an elegant underlying process. A sunflower often has 21 spirals clockwise and 34 spirals counterclockwise, or 55 clockwise and 34 counterclockwise. Larger ones can have 89 and 55. Smaller ones might have 21 spirals clockwise and 13 counterclockwise (as do some other flowers and plants). All these are “Fibonacci sequence”  numbers.  The sequence includes: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. The number of spirals is usually a number from this sequence. The reasons for this are so fascinating, I wrote it all up in a few pages that I added to my coloring book, Patterning Spirals. You can see these Fibonacci numbers in the spirals in the coloring book.

To make this coloring book, I created images with a computer mode of floral spiraling.The model shows how various spiral patterns emerge over time, and how very small changes in the turn angle can drastically change the final patterns. Here’s a long movie of the process. Here’s a very brief version of the movie. I found the spiraling animation so beautiful that I wrote a waltz to go with it.

The coloring book is for all ages, and the mindfulness exercises in it also work for all ages. If you are a parent or teacher, you will appreciate that this coloring book combines science, technology, engineering, art and math (STEAM). Likewise we can increase are scientific and aesthetic awareness of the generation of spots and stripes n nature. The material in this coloring book thus addresses STEM and STEAM educational objectives, while capturing the elegance of a natural process, and raising both mindful and scientific awareness about the natural process generating spirals.

Understanding the math and science of the spirals is one way to appreciate the beauty of the whole structure that emerges. An alternative way is to focus on the separate parts, the diamond shaped seeds. One could meditate upon each seed, one at a time, like one would do with prayer beads or a rosary, focusing on one bead at a time.  If you turn inwards to contemplate the coloring activity itself, you can cultivate mindfulness. A mindful coloring session is a focused attention on the sensations of the act of coloring in the present moment, without judgment of the final outcome. So I included in the coloring book two meditations that I adapted from mindfulness meditations by Thich Nhat Hanh, a Buddhist monk since he was sixteen. He has been teaching many forms of mindful living, mindful breathing, mindful walking, mindful eating, even mindful peacemaking, for many decades. Bringing gentle mindfulness to his life of action in a world full of conflict, Thich Nhat Hahn has inspired countless numbers, and inspired Martin Luther King to nominate him for a Nobel Peace Prize.  I have practiced his meditations for many years and they have brought much joy to my life.  So, I naturally tend to bring his approach to this coloring book.

I think many people might find mindfulness of coloring spirals to be very different from the awareness of the science of spirals. Letting all concepts slip away and turning attention inwards is at the heart of mindfulness meditation, typically. Nonetheless, I think mindfulness and appreciation of the math and science of our world ultimately can support one another.  Thich Nhat Hanh brings into his tangerine meditation the nourishing of the sun and soil, and ecological interdependence shows up in many of his guided meditations. The Dalai Lama has an insatiable appetite for science, particularly brain science. Now I see a recent research piece, published in the respected Journal of Developmental Psychology (Schonert-Reichl et al), found kids put into a mindfulness meditation course ended up with higher math scores. The study assigned children to either four months of a mindfulness program, or four months of the standard “social responsibility” program used in (Canadian) public schools. The meditation included mindful eating and social perspective taking as well as mindful breathing. The kids with the mindfulness intervention had 15% higher math scores, demonstrated 24% more appropriate social behaviors and 24% less aggressive behaviors. We may do mindfulness for the joy it, yet reap other benefits too.


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Carsley D, Heath NL, Fajnerova S. 2015. Effectiveness of a classroom mindfulness coloring activity for test anxiety in children. Journal of Applied School Psychology, 31: 239–255.

Curry NA,  Kasser T. 2005. Can coloring mandalas reduce anxiety? Art Therapy: Journal of the American Art Therapy Association, 22 (2): 81–85.

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Eaton J, Tieber C. 2017. The Effects of Coloring on Anxiety, Mood, and Perseverance: Journal of the American Art Therapy Association, 34 (1): 42-46.

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Nhat Hanh T. 1991. Peace Is Every Step: The Path of Mindfulness in Everyday Life. New York: Bantam Books.

Schonert-Reichl KA, Oberle E, Lawlor MS, Abbott DT, Thompson K, Oberlander TF, Diamond A. 2015. Enhancing cognitive and social–emotional development through a simple-to-administer mindfulness-based school program for elementary school children: A randomized controlled trial. Developmental Psychology, 51(1): 52-66.
Swinton J, Ochu E. 2016. Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment. Royal Society Open Science 3: 160091.

Van der Vennet R, Serice S. 2012. Can coloring mandalas reduce anxiety? A replication study.  Journal of the American Art Therapy Association, 29 (2): 87–92.