From 1f703b8ff31bd982c5ea6d00a09f10e33a0fe03c Mon Sep 17 00:00:00 2001 From: Permondes Date: Wed, 31 Dec 2025 10:09:21 +0100 Subject: [PATCH] LACE: document re-structured, consistent syntax; Aplaca60 Examples: Speed of bullet when it reaches the ground LACE: document re-structured, consistent syntax Applications: alpaca60: Arneodo chaotic oscilator --- Analog Engine Example Applications.odt | Bin 2162389 -> 2204586 bytes Language for Analog Computing Engines.odt | Bin 56560 -> 105652 bytes scripts/Bullet.LACE | 27 +++++++++ scripts/alpaca60 Arneodo.LACE | 65 ++++++++++++++++++++++ 4 files changed, 92 insertions(+) create mode 100644 scripts/Bullet.LACE create mode 100644 scripts/alpaca60 Arneodo.LACE diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example Applications.odt index d26398f6050517b24bb8c60899af10cd6d60a901..ba5cfc21b3637e357c59377330c0942751722418 100644 GIT binary patch delta 162454 zcmagG1yoes_dhJ6fJz96NT+~+poDbC(1<7<(j_1*c~O*RaOfI9KpIBrMg{5aMya6& 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initial vertical speed + +iintegrate (-g, 10*: friction) -> -v + IC: v0 +iintegrate (-v) -> z + +invert -v -> v + +multiply (-v, -v) -> v^2 +cmultiply (k, v^2) -> kv^2 + +# make sure friction acts against the direction of propagation +invert kv^2 -> -kv^2 +compare v -> friction + GT0: -kv^2 # v > 0 => moving upwards + LT0: kv^2 # v < 0 => moving downwards + +output (v) -> out.x +Output (friction) -> out.y +output (z) -> out.z diff --git a/scripts/alpaca60 Arneodo.LACE b/scripts/alpaca60 Arneodo.LACE new file mode 100644 index 0000000..db46c99 --- /dev/null +++ b/scripts/alpaca60 Arneodo.LACE @@ -0,0 +1,65 @@ +# Arneodo-Attractor (alpaca_60) +# x' = y, x0 = 1 +# y' = z, y0 = 1 +# z' = a*x-b*y-z-c*x^3, z0=0 +# a=5,5; b=3,5; c=1 +# +# SCALING +# the problem is patched as designed, but x runs out of range +# Trial: x = 5*xn (xn = new x), y = 10*yn, z = 15*zn +# 5*xn' = 10*y => xn' = 2*y +# 10*y' = 15*zn => y' = 1,5*z +# 15*zn' = a*5*xn-b*10*yn-15*zn-c*(5*xn)^3 => z' = a*5/15*xn-b*10/15*yn-15/15*zn-c*125/15*xn^3 +# +# xn' = d1*y +# yn' = e1*z +# zn' = a1*xn-b1*yn-zn-c1*xn^3 +# +# a1 = a*5/15 = 1,83 +# b1 = b*10/15 = 2,33 +# c1 = c*5^3/15 = 8,33 +# d1 = 2 +# e1 = 1,5 +# +# in the following, the original terms are being used, + +coefficient.1 -> a/10 # 0,183 -> better results with 0,154 +coefficient.2 -> b/10 # 0,233 +coefficient.3 -> c/10 # 0,833 +coefficient.4(+1) -> x0 # 0,200 +coefficient.5(+1) -> y0 # 0,100 +coefficient.6(+1) -> z0 # 0 +coefficient.7 -> d/10 # 0,200 +coefficient.8 -> e/10 # 0,150 + +iintegrate 10*: x' -> -x + IC: x0 +iintegrate 10*: y' -> -y + IC: y0 +iintegrate z' -> -z + IC: z0 + +invert -x -> x + +invert -y -> y +cmultiply y, d/10 -> d/10*y +assign d/10*y -> x' + +invert -z -> z +cmultiply z, e/10 -> e/10*z +assign e/10*z -> y' + +cmultiply x, a/10 -> a/10*x +cmultiply -y, b/10 -> -b/10*y + +multiply -x, -x -> x^2 +multiply x^2, -x -> -x^3 +cmultiply -x^3, c/10 -> -c/10*x^3 + +isum 10*:a/10*x, 10*:-b/10*y, -z, 10*:-c/10*x^3 -> -(a*x-b*y-z-c*x^3) +invert -(a*x-b*y-z-c*x^3) -> a*x-b*y-z-c*x^3 +assign a*x-b*y-z-c*x^3 -> z' + +output x -> out.x +output y -> out.y +output z -> out.z -- 2.47.3