math and architecture meets the intricate designs of botany, dr grordbort presents: the deadliest game

An architecture graduate constructs intricate botanical illustrations using the computer graphics programs intended to design buildings

What’s the difference between a 100-story skyscraper towering over a bustling metropolis and a 2-inch flower blooming in the countryside? To architecture-student-turned-artist Macoto Murayama, not a whole lot.

“[The flower] is organic and is rather different from architecture [in that way],” Murayama writes in an email (translated by Rodion Trofimchenko, a curator at the Frantic Gallery in Tokyo, Japan, where Murayama shows his work). “[But] when I looked closer into a plant that I thought was organic, I found in its form and inner structure, hidden mechanical and inorganic elements.”

Intrigued, Murayama began applying the computer graphics programs and techniques he had learned while studying architecture at Miyagi University of Education in Sendai to illustrate, in meticulous detail, the anatomy of flowers. After choosing a flower, purchased at the flower shop or picked up on the side of a road, he carefully dissects it, cutting off its petals with a scalpel and extracting the ovary and other internal structures. He then sketches what he sees, photographs it, and models it on the computer using 3dsMAX software, a program typically used by architects and animators. Finally, he creates a composition of the different parts in Photoshop, and uses Illustrator to add measurements and other labels.

Satsuki azalea by Macoto Murayama

There is a slide show featuring seven of Macoto’s amazing works at the link. The idea that flowers are structural models whose shapes follow a mathematical pattern is not new. Most flowers follow a distinct pattern. A rose for instance:  rhodonea curve is a sinusoid plotted in polar coordinates. Up to similarity, these curves can all be expressed by a polar equation of the form

\!\,r=\cos(k\theta).
  • 2k petals if k is even, and
  • k petals if k is odd.

When k is even, the entire graph of the rose will be traced out exactly once when the value of θ changes from 0 to 2π. When k is odd, this will happen on the interval between 0 and π. (More generally, this will happen on any interval of length 2π for k even, and π for k odd.)

If k ends in 1/2 (ex: 0.5, 2.5), the curve will be rose shaped with 4k petals.

If k ends in 1/6 or 5/6 and is greater than 1 (ex: 1.16666667, 2.8333333), the curve will be rose shaped with 12k petals.

Rose curves defined by r = sin kθ, for various values of k=n/d.

Seeing the numbers or patterns in the life around us is not some kind of sterile reductionism. At least not to me. The patterns and figuring them out adds some mystery. The numbers or equations themselves are hidden. To recognize the pattern and find an equation that describes it is like taking a journey. As often happens with journeys the best part is not always arriving at the destination, but the journey itself.

This video fits in with the flower story. Dr Grordbort Presents: The Deadliest Game. Some fun live action combined with animation reminiscent of the kind of old B-movies that Indian Jones was based on. This one features a comic version of the worse of 19th century British upper-class mentality, a mix of imperialism and taking nature specimens without much much regard for life or consequences.

A short film from Media Design School based on the sci-fi world of Dr Grordbort created by writer and artist Greg Broadmore from Weta Workshop.

The live action/CGI film was created by 11 students over 22 weeks under the direction of 3D animation program leader James Cunningham.

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