"Underside of hind wing brilliant metallic blue with orange and black spots" [1]. More precisely, the spots, usually seven of them, have orange centers with predominantly black circumference. However, the surroundings of an orange spot rarely amount to a fully black annulus, and are typically dappled with a white obstruction. On the fifth spot from anterior to posterior, you will often find not just one, but two dabs of white. This description can be checked against numerous digital photographs, and even against video evidence [2-3], but the most fun is to go out in nature and find one yourself [4]! Or if you haven't any in your region, maybe check the history books going back as far as the late 1700s [5]. Most of the more recent articles I could find were more about chemical defence, than chemical morphogenesis. The later was an interest of Alan Turing in the years before his untimely death. These days, not only can we take more and more data integrals, it should also be easier to work out the theory using all sorts of computer algorithms. Any thoughts? Cheers --Brad [1] https://scholarworks.uark.edu/cgi/viewcontent.cgi?article=3106&context=jaas [2] https://www.butterfliesandmoths.org/species/Battus-philenor [3] https://www.youtube.com/watch?v=u2cE86AA1q0&app=desktop [4] https://0x0.st/zO7w.JPG [5] http://entnemdept.ufl.edu/creatures/bfly/pipevine_swallowtail.htm
On Fri, Aug 9, 2019 at 12:48 PM Brad Klee <bradklee@gmail.com> wrote:
Most of the more recent articles I could find were more about chemical defence, than chemical morphogenesis. The later was an interest of Alan Turing in the years before his untimely death. These days, not only can we take more and more data integrals, it should also be easier to work out the theory using all sorts of computer algorithms. Any thoughts? There's a lot of recent work on reaction-diffusion, both within the biology community and in computer graphics. Two seminal papers from 1991 set off a wave of computer graphics research: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.86.298&rep=rep1&typ... ttps://www.cc.gatech.edu/~turk/my_papers/reaction_diffusion.pdf
Hi Tom, Thanks, these look helpful. I will read in more detail later, but for now I am in the field working on Spicebush and Tiger varieties. I found some roadkill specimens, and on close observation a hypothesis occurred to me that something like tie-dye is going on during chrysalis phase. So we probably need to do the RD equations on a folded surface. Has this ever been done? Got to run, more sample points to take. Cheers ++Brad
On Aug 9, 2019, at 3:43 PM, Tom Duff <td@pixar.com> wrote:
On Fri, Aug 9, 2019 at 12:48 PM Brad Klee <bradklee@gmail.com> wrote:
Most of the more recent articles I could find were more about chemical defence, than chemical morphogenesis. The later was an interest of Alan Turing in the years before his untimely death. These days, not only can we take more and more data integrals, it should also be easier to work out the theory using all sorts of computer algorithms. Any thoughts? There's a lot of recent work on reaction-diffusion, both within the biology community and in computer graphics. Two seminal papers from 1991 set off a wave of computer graphics research: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.86.298&rep=rep1&typ... ttps://www.cc.gatech.edu/~turk/my_papers/reaction_diffusion.pdf
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If you’re in the Bay Area, Brad, I have lots of specimens you can look at. I was a collector in previous life. I also have a great book that Vince Matsko gave me: The Development and Evolution of Butterfly Wing Patterns, by H. Frederik Nijhout. Scott
On 2019/08/10, at 10:17, bradklee@gmail.com wrote:
Hi Tom,
Thanks, these look helpful. I will read in more detail later, but for now I am in the field working on Spicebush and Tiger varieties.
I found some roadkill specimens, and on close observation a hypothesis occurred to me that something like tie-dye is going on during chrysalis phase.
So we probably need to do the RD equations on a folded surface. Has this ever been done?
Got to run, more sample points to take.
Cheers ++Brad
On Aug 9, 2019, at 3:43 PM, Tom Duff <td@pixar.com> wrote:
On Fri, Aug 9, 2019 at 12:48 PM Brad Klee <bradklee@gmail.com> wrote:
Most of the more recent articles I could find were more about chemical defence, than chemical morphogenesis. The later was an interest of Alan Turing in the years before his untimely death. These days, not only can we take more and more data integrals, it should also be easier to work out the theory using all sorts of computer algorithms. Any thoughts? There's a lot of recent work on reaction-diffusion, both within the biology community and in computer graphics. Two seminal papers from 1991 set off a wave of computer graphics research: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.86.298&rep=rep1&typ... ttps://www.cc.gatech.edu/~turk/my_papers/reaction_diffusion.pdf
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More recent (probably) is "Diversity and Evolution of Butterfly Wing Patterns: An Integrative Approach" by Toshio Sekimura, H. Frederik Nijhout Arie Bos
-----Oorspronkelijk bericht----- Van: math-fun <math-fun-bounces@mailman.xmission.com> Namens Scott Vorthmann Verzonden: zaterdag 10 augustus 2019 19:23 Aan: math-fun <math-fun@mailman.xmission.com> Onderwerp: Re: [math-fun] Papilio philenor
If you’re in the Bay Area, Brad, I have lots of specimens you can look at. I was a collector in previous life. I also have a great book that Vince Matsko gave me: The Development and Evolution of Butterfly Wing Patterns, by H. Frederik Nijhout.
Scott
On 2019/08/10, at 10:17, bradklee@gmail.com wrote:
Hi Tom,
Thanks, these look helpful. I will read in more detail later, but for now I am in the field working on Spicebush and Tiger varieties.
I found some roadkill specimens, and on close observation a hypothesis occurred to me that something like tie-dye is going on during chrysalis phase.
So we probably need to do the RD equations on a folded surface. Has this ever been done?
Got to run, more sample points to take.
Cheers ++Brad
On Aug 9, 2019, at 3:43 PM, Tom Duff <td@pixar.com> wrote:
On Fri, Aug 9, 2019 at 12:48 PM Brad Klee <bradklee@gmail.com> wrote:
Most of the more recent articles I could find were more about chemical defence, than chemical morphogenesis. The later was an interest of Alan Turing in the years before his untimely death. These days, not only can we take more and more data integrals, it should also be easier to work out the theory using all sorts of computer algorithms. Any thoughts? There's a lot of recent work on reaction-diffusion, both within the biology community and in computer graphics. Two seminal papers from 1991 set off a wave of computer graphics research: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.86.298&rep=r ep1&type=pdf ttps://www.cc.gatech.edu/~turk/my_papers/reaction_diffusion.pdf
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I am now studying both of the Nijhout books, and reading about Japanese cultural meaning of 蝶 "Chou". But I also found this: https://social.mbl.edu/watching-a-butterfly-wing-get-its-color Wow, incredible data! This will really help theorists get to new works. --Brad On Mon, Aug 12, 2019 at 6:24 AM R B <bossipm@outlook.com> wrote:
More recent (probably) is "Diversity and Evolution of Butterfly Wing Patterns: An Integrative Approach" by Toshio Sekimura, H. Frederik Nijhout Arie Bos
Brad:
So we probably need to do the RD equations on a folded surface. Has this ever been done?
Check out Ready (runs on Windows, Mac, Linux): https://github.com/GollyGang/ready It lets you explore RD systems on arbitrary meshes. Andrew
participants (6)
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Andrew Trevorrow -
Brad Klee -
bradklee＠gmail.com
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R B -
Scott Vorthmann -
Tom Duff