Fractal generator and mathematics inside us

Three elements: fire, water and Milla Jovovich (below there will be speculations about the process of its recreation in the film "The Fifth Element")
Three elements: fire, water and Milla Jovovich (below there will be speculations about the process of its recreation in the film "The Fifth Element")

I invite you to taste a salad of diverse, but unexpectedly related topics:





  • Why do we like symmetry and fractals? And how does this affect survival?





  • How is mathematics related to embryonic development?





  • How many old programs still need to be saved from the relentless time?





  • Beauty contest among fractals.





Isn't it strange that we are pleased to see symmetrical objects? But if there is too much symmetry, then for some reason it starts to annoy. Perhaps we will find a meaning in this if we come closer to understanding the principles of the formation of everything around us, which are isolated by the brain. And for this we will play with the next fractal generator, in which it is convenient to create almost everything: from islands in the ocean and clouds in the sky to the circulatory system, from galaxies to  wallpapers on the desktop of the  smallest particles.





Heart mark from the dough stirring blade
Heart mark from the dough stirring blade

, , . , - , .





, - , . , . ?





, , «». , — , . , - :





Illustration from the article Higgs Boson and Mass Endowment
 

, , - . , . , // , , - , .





, , . . , ?





, - ? , . : , . , , , - .





, - . , - , . , .





. . , , , , // .





, , , . , , . , , , , .





?

. , . , , , . , .





, «», - ( « ?», ).





, , , , . , , , .





, , , .





Wonderful transformation of one pixel into a proud sounding person

, , - , ( IFS  ), (. «L- »  «L-Systems — ») . , , , . , . , .





, — 1x1 3x3 :





Nine rules to illustrate the embryonic development process

, ( ), ( ), ( ) .. , ( ) — , .





, . , ( ) -- , () . (.. 3x3 ). , , .





! , . Depth, . , , . !





, , . : {"depth":3,"n":3,"rules":[[106,3,706,4,3,404,6,5,406], [1,1,1,1,1,1,1,1,1], [1,308,7,1,1,7,1,708,7], [8,7,408,308,7,508,2,7,402], [608,7,408,1,1,1,1,1,1], [708,502,108,7,1,7,7,1,7], [1,1,1,1,1,1,1,1,8], [7,7,7,7,7,7,7,7,7],[1,1,708,8,7,7,7,7,7]], "colors":["#ff0000", "#ffffff", "#f7bfbf", "#E6B333", "#3366E6", "#999966", "#99FF99", "#d24b81", "#e585bd"]}.





: 2x2:





Doesn't look like clouds?  In my opinion, it looks much more like cirrus clouds than that red man on Leela.
? -, , .

, , , , , . , , .





, JSON ,  :

{"depth":10,"n":2,"rules":[[200,1,100,600],[1,102,100,100],[2,102,2,2]],"colors":["#9fbae9","#735cc7","#ffffff"]}







   ( , , ):





, , (ln 8/ln 3 ~ 1,89), , . , , . ! , , .





 Changer2 (​1997 , CC0 v.1.0 ), Changer ( , , ). Changer2 , Windows . ( ):





, , «Jelly no Puzzle» (  - ).   . , , , .





, , , , . , . , , . , ?





Still from the movie "The Hudsucker Proxy"
«The Hudsucker Proxy»

Changer2 , 7 107 . , - , 30-40 , , , , , .





! . JavaScript ( 1024x1024 , ). , , !





, . - : , .





, . , , , !





, , , :





  • ( );





  • (- );





  • ,   -2;





  • (Random IFS, kNN, Escape-Time Algorithm);





  • — (3Blue1Brown);





  • , ;





  • TED: « »;





  •  (- ; ,   ).





Send your fractals in the comments! The full address of the fractal can be taken either in the address bar of the browser or by copying it from the link "Link to this configuration" on the generator page . The easiest way to get an image is by selecting the item "Copy image" or "Save image as ..." in the context menu of the generated image. The browser's Back button works like an Undo, so you can always roll back to the previous state of your ruleset. If you try to build an image with more than 2200x2200 pixels, the system will ask you again, since it can still take a long time (to work in such high quality, I recommend disabling automatic redrawing).








All Articles