Category: Thinking

Frac­tals are inher­ent­ly nat­ur­al; and nature loves to repeat pat­terns. This real­ly isn’t a sur­prise, because every­one knows that there is alot of sym­me­try [which is a bit dif­fer­ent than pat­tern­ing, yes] in nat­ur­al objects. It’s like in π where the Gold­en Ratio [a sort of frac­tal] can be found every­where. For years one of my doo­dling habits has been, unknow­ing­ly, an echo of the Gold­en Ratio. I draw a right tri­an­gle and then sec­tion it off by draw­ing a line per­pen­dic­u­lar to the hypotenuse from the right angle of the tri­an­gle. The result is two more right tri­an­gles, which I then do the same thing to. Small­er and small­er and small­er. Anoth­er way of describ­ing frac­tals uses the exam­ple of a coast­line, if you’re mea­sur­ing the length of a coast­line, the clos­er you get the longer the coast­line becomes. A finite area bound­ed by an infi­nite line.

Asymp­totes come to mind here as well, and the old saw about a frog jump­ing halfway to the pond with each jump. He’ll nev­er reach the pond, math­e­mat­i­cal­ly speak­ing, because he only halves the dis­tance remain­ing with each jump. This is why I can nev­er know any­thing, despite the fact that I’ve learned so very much in almost 25 years, I’m still only halfway to wher­ev­er there is. This might be a very good expla­na­tion for why we can’t ever real­ly know God or reach per­fec­tion on our own, but I’m way off track at this point.

Branch­es were the impe­tus to write this post. So many things branch, and branch the same way, that it gives me the good willies. When I tru­ly real­ized that there has to be a rea­son behind the sim­i­lar­i­ty between rivers and trib­u­taries, the branch­es of a tree, our veins, cap­il­lar­ies and arter­ies it was one of those minor mind­blow­ing things that only real­ly occur to me when I see some­thing ubiq­ui­tous and mun­dane as if for the first time. The sphere is anoth­er reoc­cur­ing pat­tern, from sub­atom­ic par­ti­cles up to plan­ets- rain is spher­i­cal, or would be with­out the work of grav­i­ty. This makes me think that size does not mat­ter. Anoth­er thought I had the oth­er day, atoms are most­ly emp­ty space. The uni­verse is most­ly emp­ty space. Sci­ence has this idea of dark mat­ter, and they think it must fill the “emp­ty space” of the uni­verse. I won­der if any­one has thought to look in the emp­ty space of atoms.

Chris Coyne has made a math­e­mat­i­cal pro­gram­ming lan­guage [redun­dant, I know] that can cre­ate beau­ti­ful pic­tures, includ­ing some with branch­es.