User blog:B1mb0w/Sequence Generator Code

Sequence Generator Code
I am developing general purpose code to generate long strings of finite integers according to rules that can be written using the correct syntax.

This code is being used by my Beta Function code.

WORK IN PROGRESS

Example Sequence Generator Code
Here is example code. More information on the syntax and logic will be provided.

b = (V_r='Beta Function r Parameter',V_v='Beta Function v Parameter',h_0)

h = (C_d<2,C_d=(0:C_x<V_v-U_x,(E_h=1,f_0)))

f = (g_x,g_x=(0:h_u<E_h,(h_U<E_h,E_h=C_d..h_U,f_x+1<g_x)))

g = (C_q<V_v+1,C_q=(0:h_x<E_h,1:t_a,(g_[q]<C_q..g_q-1,n_0<C_q-1,t_a)))

t = (h_T<E_h,g_E<C_q..t_x,g_C<C_q..h_T,g_x<C_q..g_E)

WORK IN PROGRESS

Example Sequences (in JSON format)
Sequences are generated using JSON format. A good JSON Viewer can be found here.

Here are some examples:

\(\beta(0,2) = 0\) ==

{"V_r":0,"V_v":2,"h_0":{"C_d":0,"C_0":0}}

\(\beta(0.5,2) = 1\) ==

{"V_r":0.5,"V_v":2,"h_0":{"C_d":0,"C_0":1}}

\(\beta(1,2) = 2\) ==

{"V_r":1,"V_v":2,"h_0":{"C_d":1,"E_h":1,"f_0":{"g_0":{"C_q":0,"h_0":{"C_d":0,"C_0":0}},"h_u":{"C_d":0,"C_u":0}}}}

\(\beta(1.2,2) = 3\) ==

{"V_r":1.2,"V_v":2,"h_0":{"C_d":1,"E_h":1,"f_0":{"g_0":{"C_q":0,"h_0":{"C_d":0,"C_0":0}},"h_u":{"C_d":0,"C_u":1}}}}

\(\beta(1.5,2) = 4\) ==

{"V_r":1.5,"V_v":2,"h_0":{"C_d":1,"E_h":1,"f_0":{"g_0":{"C_q":0,"h_0":{"C_d":0,"C_0":1}},"h_U":{"C_d":0,"C_U":0},"E_h":"0..5","f_1":{"g_1":{"C_q":0,"h_1":{"C_d":0,"C_1":0}},"h_u":{"C_d":0,"C_u":0}}}}}

\(\beta(1.6,2) = 5\) ==

{"V_r":1.6,"V_v":2,"h_0":{"C_d":1,"E_h":1,"f_0":{"g_0":{"C_q":0,"h_0":{"C_d":0,"C_0":1}},"h_U":{"C_d":0,"C_U":0},"E_h":"0..5","f_1":{"g_1":{"C_q":0,"h_1":{"C_d":0,"C_1":0}},"h_u":{"C_d":0,"C_u":1}}}}}

\(\beta(1.7,2) = 6\) ==

{"V_r":1.7,"V_v":2,"h_0":{"C_d":1,"E_h":1,"f_0":{"g_0":{"C_q":0,"h_0":{"C_d":0,"C_0":1}},"h_U":{"C_d":0,"C_U":0},"E_h":"0..5","f_1":{"g_1":{"C_q":0,"h_1":{"C_d":0,"C_1":0}},"h_u":{"C_d":1,"E_h":1,"f_0":{"g_0":{"C_q":0,"h_0":{"C_d":0,"C_0":0}},"h_u":{"C_d":0,"C_u":0}}}}}}}

\(\beta(1.9,2) = 7\) ==

{"V_r":1.9,"V_v":2,"h_0":{"C_d":1,"E_h":1,"f_0":{"g_0":{"C_q":0,"h_0":{"C_d":0,"C_0":1}},"h_U":{"C_d":0,"C_U":0},"E_h":"0..5","f_1":{"g_1":{"C_q":0,"h_1":{"C_d":0,"C_1":0}},"h_u":{"C_d":1,"E_h":1,"f_0":{"g_0":{"C_q":0,"h_0":{"C_d":0,"C_0":0}},"h_u":{"C_d":0,"C_u":1}}}}}}}

Test Bed
Initial Attempts will be presented here until the code is stabilised:

\(\beta(0,2) = 0 = 0\)

\(\beta(0.5,2) = 1 = 1\)

\(\beta(1,2) = 2 = 2\)

\(\beta(1.2,2) = 3 = 3\)

\(\beta(1.5,2) = 4 = 4\)

\(\beta(1.6,2) = 5 = 5\)

\(\beta(1.7,2) = 6 = 6\)

\(\beta(1.9,2) = 7 = 7\)

\(\beta(2.0001,2) = f_{\omega}(2) = 8\)

\(\beta(2.05,2) = f_{\omega}(2) + 1 = 9\)

\(\beta(2.1,2) = f_{\omega}(2) + 2 = 10\)

\(\beta(2.125,2) = f_{\omega}(2) + 3 = 11\)

\(\beta(2.135,2) = f_{\omega}(2) + 4 = 12\)

\(\beta(2.15,2) = f_{\omega}(2) + 5 = 13\)

\(\beta(2.16,2) = f_{\omega}(2) + 6 = 14\)

\(\beta(2.17,2) = f_{\omega}(2) + 7 = 15\)

\(\beta(2.2,2) = f_{\omega}(2).2 = 16\)

\(\beta(2.21,2) = f_{\omega}(2).2 + 1 = 17\)

\(\beta(2.23,2) = f_{\omega}(2).2 + 2 = 18\)

\(\beta(2.24,2) = f_{\omega}(2).2 + 3 = 19\)

\(\beta(2.2425,2) = f_{\omega}(2).2 + 4 = 20\)

\(\beta(2.245,2) = f_{\omega}(2).2 + 5 = 21\)

\(\beta(2.247,2) = f_{\omega}(2).2 + 6 = 22\)

\(\beta(2.25,2) = f_{\omega}(2).2 + 7 = 23\)

\(\beta(2.255,2) = f_{\omega}(2).2 + f_{\omega}(2) = 24\)

\(\beta(2.28,2) = f_{\omega}(2).4 = 32\)

\(\beta(2.2965,2) = f_{\omega}(2).4 + f_{\omega}(2) = 40\)

\(\beta(2.3,2) = f_{\omega}(2).4 + f_{\omega}(2).2 = 48\)

\(\beta(2.30175,2) = f_{\omega}(2).4 + f_{\omega}(2).2 + f_{\omega}(2) = 56\)

\(\beta(2.303,2) = f_{\omega}(2).8 = 64\)

\(\beta(2.33,2) = f_{\omega}(2).16 = 128\)

\(\beta(2.343,2) = f_{\omega}(2).32 = 256\)

\(\beta(2.355,2) = f_{\omega}(2).64 = 512\)

\(\beta(2.366,2) = f_{\omega}(2).128 = 1024\)

\(\beta(2.38,2) = f_{2}(f_{\omega}(2)) = 2048\)

\(\beta(2.405,2) = f_{2}(f_{\omega}(2)).2 = 4096\)

\(\beta(2.4177,2) = f_{2}(f_{\omega}(2)).4 = 8192\)

\(\beta(2.4194,2) = f_{2}(f_{\omega}(2)).8 = 16384\)

\(\beta(2.4207,2) = f_{2}(f_{\omega}(2)).16 = 32768\)

\(\beta(2.4216,2) = f_{2}(f_{\omega}(2)).32 = 65536\)

\(\beta(2.4224,2) = f_{2}(f_{\omega}(2)).64 = 131072\)

\(\beta(2.4233,2) = f_{2}(f_{\omega}(2)).128 = 262144\)

\(\beta(2.424,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2)}) = 524288\)

\(\beta(2.4249,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2) + 1}) = 1048576\)

\(\beta(2.4256,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2) + 2}) = 2097152\)

\(\beta(2.426,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2) + 3}) = 4194304\)

\(\beta(2.4264,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2) + 4}) = 8388608\)

\(\beta(2.4266,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2) + 5}) = 16777216\)

\(\beta(2.4268,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2) + 6}) = 33554432\)

\(\beta(2.42705,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2) + 7}) = 67108864\)

\(\beta(2.4273,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2).2}) = 134217728\)

\(\beta(2.4277,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2).2 + 1}) = 268435456\)

\(\beta(2.42805,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2).2 + 2}) = 536870912\)

\(\beta(2.42815,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2).2 + 3}) = 1073741824\)

\(\beta(2.428245,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2).2 + 4}) = 2147483648\)

\(\beta(2.428295,2) = f_{2}(f_{\omega}(2)).(2^{f_{\omega}(2).2 + 5}) = 4294967296\)

\(\beta(2.432,2) = f_{2}^2(f_{\omega}(2))\)

\(\beta(2.445,2) = f_{2}^3(f_{\omega}(2))\)

\(\beta(2.4575,2) = f_{2}^4(f_{\omega}(2))\)

\(\beta(2.464,2) = f_{2}^5(f_{\omega}(2))\)

\(\beta(2.471,2) = f_{2}^6(f_{\omega}(2))\)

\(\beta(2.477,2) = f_{2}^7(f_{\omega}(2))\)

\(\beta(2.485,2) = f_{3}(f_{\omega}(2))\)

\(\beta(2.5385,2) = f_{3}^2(f_{\omega}(2))\)

\(\beta(2.566,2) = f_{3}^4(f_{\omega}(2))\)

\(\beta(2.58,2) = f_{3}^6(f_{\omega}(2))\)

\(\beta(2.595,2) = f_{4}(f_{\omega}(2))\)

\(\beta(2.6363,2) = f_{4}^4(f_{\omega}(2))\)

\(\beta(2.652,2) = f_{5}(f_{\omega}(2))\)

\(\beta(2.71,2) = f_{6}(f_{\omega}(2))\)

\(\beta(2.768,2) = f_{7}(f_{\omega}(2))\)

\(\beta(2.85,2) = f_{\omega + 1}(2)\)

\(\beta(2.96,2) = f_{\omega + 1}(2).2\)

\(\beta(3.085,2) = f_{2}(f_{\omega + 1}(2))\)

\(\beta(3.119,2) = f_{3}(f_{\omega + 1}(2))\)

\(\beta(3.152,2) = f_{4}(f_{\omega + 1}(2))\)

\(\beta(3.1695,2) = f_{5}(f_{\omega + 1}(2))\)

\(\beta(3.1865,2) = f_{6}(f_{\omega + 1}(2))\)

\(\beta(3.204,2) = f_{7}(f_{\omega + 1}(2))\)

\(\beta(3.38,2) = f_{\omega}(f_{\omega + 1}(2))\)

\(\beta(3.4,2) = f_{\omega}(f_{\omega + 1}(2)) + 1\)

\(\beta(3.5,2) = f_{\omega}(f_{\omega + 1}(2)).(2^{f_{2}^{f_{\omega}(2).4 + f_{\omega}(2).2 + f_{\omega}(2) + 5}(f_{3}(f_{\omega}(2))) + 4})\)

\(\beta(3.6,2) = f_{f_{\omega}(2).2}^6(f_{\omega}(f_{\omega + 1}(2))).2 + 3\)

\(\beta(3.7,2) = f_{5}^3(f_{f_{\omega}(2).8}^{f_{3}^2(f_{5}^2(f_{\omega}(2))).32 + 1}(f_{\omega}^2(f_{\omega + 1}(2))))\)

\(\beta(3.8,2) = f_{2}(f_{\omega}^6(f_{\omega + 1}(2))).(2^{f_{\omega}(2).2 + 1}) + 2\)

\(\beta(3.9,2) = f_{\omega}^{f_{\omega}(2).8 + 1}(f_{\omega + 1}(2)) + f_{\omega}(2) + 7\)

\(\beta(3.95,2) = f_{3}(f_{\omega}^{f_{3}^3(f_{\omega}(2)).32 + 1}(f_{\omega + 1}(2)))\)

\(\beta(3.99,2) = f_{3}(f_{5}(f_{\omega}^{f_{7}(f_{\omega}(2)) + 3}(f_{\omega + 1}(2)))).(2^{f_{\omega}(2)}) + 1\)