Architect and illustrator Rafael Araujo combines natural subjects with visible geometric construction. Pencils, rulers, a compass and protractors help establish the framework, while the finished forms remain connected to the lines used to organize them. The golden ratio, approximately 1.618, is one specific mathematical relationship associated with the work; it should not be treated as a formula governing every shell, spiral or butterfly.
Rafael’s work is extraordinary as he leaves intact the construction lines which form the mathematical framework for his illustrations, each of which might take him as long as 100 hours to complete. The 2018 feature reported that Rafael had received requests for prints of his works to color in. From this came the idea to produce a beautiful coloring book with some of his best illustrations. To bring this project to life, Rafael and his team in Sydney created a Kickstarter campaign.
Fibonacci sequence shell
Chambered nautilus shell
Chambered nautilus shell, Photo 2
The Fibonacci Sequence
Butterfly infinite sequence
Diaethrea Sequence
DNA Butterflies Double Helix
Blue Morpho, Sequence
Butterfly infinite sequence, Photo 2
Blue Morpho, Double Helix
Danaus Plexippus, mirror
Phoebis, Triple Helix
The construction remains part of the finished image
For two positive lengths, a and b, with a larger than b, the golden-ratio relationship means that (a + b) divided by a equals a divided by b. The common value is approximately 1.618. This is a particular mathematical relationship, not a label for anything that looks balanced, curved or beautiful.
The Fibonacci sequence is related but different: each new term is the sum of the preceding two. Ratios of neighboring terms approach the golden ratio as the terms grow. A sequence of numbers, a geometric construction and a measured natural object therefore need to be distinguished even when an artwork brings them together.
A construction is a design choice
Araujo's visible guides let readers see the framework used to organize an illustration. They can be appreciated as part of the drawing rather than erased as temporary scaffolding. The relationship between that chosen framework and a real specimen would require measurements if it were being presented as a scientific claim.
For your own drawing, keep the construction lines on one version and remove them from a copy. Compare what becomes easier to follow in each. The first can explain the design's organization; the second can emphasize the finished forms. Neither needs the claim that every shell or butterfly follows an identical mathematical formula. The precision of the chosen construction is interesting enough on its own.
Construction lines left visible
Leaving the guides visible changes the drawing’s purpose. The viewer can follow a relationship between points and curves instead of seeing only a polished outline. That does not prove that a real specimen was generated by the same construction, but it makes the artist’s organizing choice available for inspection. The framework becomes a second subject, sharing the page with the natural form.
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