From bee502ae1e8662d93b90825ce7ef073eaa7b4c22 Mon Sep 17 00:00:00 2001 From: "GigaBrain.io" <32162175+gigabrainIO@users.noreply.github.com> Date: Wed, 12 Jul 2023 10:04:50 +0300 Subject: [PATCH 1/5] Added Fibonacci modulus example Added Fibonacci modulus example. Added a video reference link with the description. --- README.md | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/README.md b/README.md index 604bbf6..2cfe64b 100644 --- a/README.md +++ b/README.md @@ -299,3 +299,20 @@ Copy the JSON string below and import it to the app: "detectors":"return Array.from({length:7},(_,i)=>i-3+',0,0');" } ``` + + +#### Fibonacci modulus cliques 3D +Jacob Yatsko explains Fibonacci modulus sequences in the following video
+A New Way to Look at Fibonacci Numbers
+The following is the same view turned into a 3-dimensional view. You can easily change the modulus in the editor and redeploy the updated code.
+
+ +Copy the JSON string below and import it to the app: +```json +{ + "init":"return [[0,1]];", + "oper":"let s=[];\nfor( let p of c ) {\n let [a]=this.clone([p]);\n a[0] = a[1]\n a[1] = (p[0]+p[1]) % 10\n s.push(a);\n}\n\nreturn [s];", + "coord":"return s[1]+\"\"", + "detectors":"return ['0','1','2','3','4','5','6','7','8','9'];" +} +``` From 4a2e9effee6466c6fcf17b8ffe746205a4c8933d Mon Sep 17 00:00:00 2001 From: "GigaBrain.io" <32162175+gigabrainIO@users.noreply.github.com> Date: Wed, 12 Jul 2023 10:11:41 +0300 Subject: [PATCH 2/5] Fibonacci modulus image --- img/fibonacci3d.jpg | Bin 0 -> 130507 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 img/fibonacci3d.jpg diff --git a/img/fibonacci3d.jpg b/img/fibonacci3d.jpg new file mode 100644 index 0000000000000000000000000000000000000000..c7b54329f65c2a3c5d62a3cdab328f7d511faf5c GIT binary patch literal 130507 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z(mgTJDkfvBbXw&*pqV>jOKC~z{Zhko(hk@org9%QFRM?Ueg@G%*O0?e@#rEb~@xylN_y<$ZC`=uQI%bowA?guY?8au! zFYF#)dGlDy3T6}E$VyP~NfmNNldkUJSk&ON>Ts7Ag^E8O16Q(?RxY|z1;8WDztBuP zGW)!3o1@j!^V~(wyEVtP%V0LqF@0|<+G<7uV{)V}sEQ z0`rHm>{l9`&xtzUy-E3iQscXf%j9;Fc?&-nYZ~9rn*7f$ zZAjfRny&3DS9pYPIEozH^ByW{%62k6m;=Ps-8}DU8iF9g5B>P8uGerczfeqad${Q+ zN7Ud^z0YEbFqOqlBsWRuZHG_ikww(R?i#MMQq8W}lYWoI7A4VPmh%@&6~s5Pp}8*| z=N@l2^ki6iJKLtOzALiF9PF;Z)jGd+krS!BCoD=A;#8j-IY{PT7R3) zfMv^Bl3F%J%`S{|Pe87d%@n0C%N!-<2{N)Iy{!-zHK~Ii{6%6wSr--dbf{IUSSxxl zwm3zkda+}r=~ZPi-gCn+%N1eD!+w6|say-jA&FUI&dhfqtU>ge@OONj zRkXZx2%9&-$JA~-jZlpuGgRc&EKT{!WH&yIcW$*@J)B(?FGQ|7c?+qz55i}hNo+1o z#}pUxa2+8JBZ)mGf4_8)C3N3PewHiS@X-{TGsqVOZPPDIzA+p5T{A8RoUats>h0@z zc-Tq4flR8hDPgS7!)R(_xwLm-js~gd6`Jwgsq=l&0iGM1H7qyqV0;lB!0ovfQ+Ypq z_X?1Bfa-gBJIFDvn*qax+%ybVqEErgF7og~UeeH`Egs{A#E0ZAb>V(FUzhEHA@;!Y zTlMchH|inTrG4G%)B!Ff_bLNJ(Xd<0wr=u8*qv9xR8gJgsoYDkSP|F@)hM4ji*d|z zE-a)i$ST@;_B+I89uIrpTwa5{a)B!^Mksc^r*9-c-TFks?>2xUx{Sr_&pk_G@|Ejr z*b-NVo%E$=wfJje*(B#1;XcdrwqkChjwSC`W4j+ugsqCoa`WkuuKAoP=nwJLBaUx8 z*WC)We$BC!>Pj;Pe8npT>J4=k33Svu!ss)^(V2l1bgNdAhZK-k$w=4q>i--O`g`Gq YU+Z7-C;I(Aq2J#xE&p>H<=f={14eKU3IG5A literal 0 HcmV?d00001 From 4a63a92a1d956e01779b7334be176d0a34938aac Mon Sep 17 00:00:00 2001 From: "GigaBrain.io" <32162175+gigabrainIO@users.noreply.github.com> Date: Wed, 12 Jul 2023 21:22:57 +0300 Subject: [PATCH 3/5] Complex fibonacci modulus sequence Complex fibonacci modulus sequence --- README.md | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/README.md b/README.md index 2cfe64b..542623f 100644 --- a/README.md +++ b/README.md @@ -316,3 +316,14 @@ Copy the JSON string below and import it to the app: "detectors":"return ['0','1','2','3','4','5','6','7','8','9'];" } ``` + + +#### Complex fibonacci modulus sequence +Experimental sequence where fibonacci modulus is converted to a complex with 1/2 0.5 real part and sequence as imaginary. Graph shows a recurring structures emerging. + +Copy the JSON string below and import it to the app: +```json +{ +{"init":"return [[0,1]];","oper":"let s=[];\nfor( let p of c ) {\n let [a]=this.clone([p]);\n a[0] = a[1]\n a[1] = (p[0]+p[1])%1050\n // console.log(a)\n s.push(a);\n}\n\nreturn [s];","coord":"function convert2Rectangle(polarReal, polarAngle){\n var real = Math.cos(polarAngle*Math.PI/180)*polarReal\n var imag = Math.sin(polarAngle*Math.PI/180)*polarReal\n var RectNumber = {'real':real,'imag':imag}\n return RectNumber\n}\n\nlet dis = convert2Rectangle(0.5,s[1])\n//return Math.round(dis.real)+\"x\"+Math.round(dis.imag)+\"\"\nreturn dis.real+\"x\"+dis.imag+\"\"","detectors":"return ['0','1','2','3','4','5','6','7','8','9'];"} +} +``` From 3925abdd7ebbbbee2d9008ea29f69b1c9c76cf2e Mon Sep 17 00:00:00 2001 From: "GigaBrain.io" <32162175+gigabrainIO@users.noreply.github.com> Date: Wed, 12 Jul 2023 21:24:28 +0300 Subject: [PATCH 4/5] Update README.md --- README.md | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index 542623f..9108af7 100644 --- a/README.md +++ b/README.md @@ -324,6 +324,9 @@ Experimental sequence where fibonacci modulus is converted to a complex with 1/2 Copy the JSON string below and import it to the app: ```json { -{"init":"return [[0,1]];","oper":"let s=[];\nfor( let p of c ) {\n let [a]=this.clone([p]);\n a[0] = a[1]\n a[1] = (p[0]+p[1])%1050\n // console.log(a)\n s.push(a);\n}\n\nreturn [s];","coord":"function convert2Rectangle(polarReal, polarAngle){\n var real = Math.cos(polarAngle*Math.PI/180)*polarReal\n var imag = Math.sin(polarAngle*Math.PI/180)*polarReal\n var RectNumber = {'real':real,'imag':imag}\n return RectNumber\n}\n\nlet dis = convert2Rectangle(0.5,s[1])\n//return Math.round(dis.real)+\"x\"+Math.round(dis.imag)+\"\"\nreturn dis.real+\"x\"+dis.imag+\"\"","detectors":"return ['0','1','2','3','4','5','6','7','8','9'];"} + "init":"return [[0,1]];", + "oper":"let s=[];\nfor( let p of c ) {\n let [a]=this.clone([p]);\n a[0] = a[1]\n a[1] = (p[0]+p[1])%1050\n // console.log(a)\n s.push(a);\n}\n\nreturn [s];", + "coord":"function convert2Rectangle(polarReal, polarAngle){\n var real = Math.cos(polarAngle*Math.PI/180)*polarReal\n var imag = Math.sin(polarAngle*Math.PI/180)*polarReal\n var RectNumber = {'real':real,'imag':imag}\n return RectNumber\n}\n\nlet dis = convert2Rectangle(0.5,s[1])\n//return Math.round(dis.real)+\"x\"+Math.round(dis.imag)+\"\"\nreturn dis.real+\"x\"+dis.imag+\"\"", + "detectors":"return ['0','1','2','3','4','5','6','7','8','9'];" } ``` From cd5b0e5a9f339e51570776e8de06f2257039eeea Mon Sep 17 00:00:00 2001 From: "GigaBrain.io" <32162175+gigabrainIO@users.noreply.github.com> Date: Sat, 15 Jul 2023 10:41:22 +0300 Subject: [PATCH 5/5] Mandelbrot fibonacci modulus view Experimenting with Mandelbrot function and Fibonacci sequence --- README.md | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/README.md b/README.md index 9108af7..ee8634c 100644 --- a/README.md +++ b/README.md @@ -330,3 +330,13 @@ Copy the JSON string below and import it to the app: "detectors":"return ['0','1','2','3','4','5','6','7','8','9'];" } ``` + +#### Mandelbrot fibonacci modulus sequence +Experimental combination of repeating fibonacci sequence with modulus 50 and the fibonacci sequence is inputed as mandelbrot pixel positions with height and width of 1000 pixels mandelbrot. + +The fractality should emerge between the nodes of the mandelbrot pixel node 80 and the outside pixels nodes 1,2,3. + +Copy the JSON string below and import it to the app: +```json +{"init":"this.MAX_ITERATION = 80\nthis.REAL_SET = { start: -2, end: 1 }\nthis.IMAGINARY_SET = { start: -1, end: 1 }\n\nthis.mandelbrot = function mandelbrot(c) {\n let z = { x: 0, y: 0 }, n = 0, p, d;\n do {\n p = {\n x: Math.pow(z.x, 2) - Math.pow(z.y, 2),\n y: 2 * z.x * z.y\n }\n z = {\n x: p.x + c.x,\n y: p.y + c.y\n }\n d = Math.sqrt(Math.pow(z.x, 2) + Math.pow(z.y, 2))\n n += 1\n } while (d <= 2 && n < this.MAX_ITERATION)\n return [n, d <= 2]\n}\n\nreturn [[0,1]];","oper":"let s=[];\nfor( let p of c ) {\n let [a]=this.clone([p]);\n a[0] = a[1]\n a[1] = (p[0]+p[1]) % 500\n s.push(a);\n}\n\nreturn [s];","coord":"const WIDTH = 1000\nconst HEIGHT = 1000\nlet complex = {\n x: this.REAL_SET.start + (s[0]/WIDTH) * (this.REAL_SET.end - this.REAL_SET.start),\n y: this.IMAGINARY_SET.start + (s[1]/HEIGHT) * (this.IMAGINARY_SET.end - this.IMAGINARY_SET.start)\n }\nconsole.log(\"Mandel \", s,\" - \", complex, \" -> \", this.mandelbrot(complex))\nlet [mandel, isMandelbrotSet] = this.mandelbrot(complex)\n\nreturn mandel+\"\"","detectors":"return ['80','1','2','3','4','5','6','7','8','9'];"} +```