Monte Carlo and Metropolis algorithm added.

16- Numberical Integration.jl

@@ -0,0 +1,38 @@
+### A Pluto.jl notebook ###
+# v0.19.27
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ 02ba7cbc-468d-11ee-2deb-2d1be28da1c0
+md"""
+# Numberical Integration
+
+There is a simple way of calculation of an integral: using the defenition of integration. For function $f(x)$, we have the integral
+
+$I = \int_{a}^{b} f(x) \mathrm{d}x = \sum_{i=1}^{N} f(x_i) h$
+
+Where $x_i = a + hi$. The key idea is that if we reduce the value of $h$, it'll be decrease the error $\Delta$, but if we continue, $\Delta$ will increase!
+
+Lets do an experiment.
+"""
+
+# ╔═╡ ce049874-6be1-4b69-b846-186e047f9579
+"integral of function `f` from `a` to `b`"
+function integral(f::Function, a::Float64, b::Float64, N::Int64)
+	h = (a+b)/N
+	X = a:h:b
+	I = sum(h*X)
+end
+
+# ╔═╡ 7ab92ecf-e2b5-4b97-991a-302dc5399917
+f(x) = x.^2
+
+# ╔═╡ 94a22398-cb45-40b9-8810-a564e58d7856
+I = integral(f, 0.0, 2.0, 10)
+
+# ╔═╡ Cell order:
+# ╟─02ba7cbc-468d-11ee-2deb-2d1be28da1c0
+# ╠═ce049874-6be1-4b69-b846-186e047f9579
+# ╠═7ab92ecf-e2b5-4b97-991a-302dc5399917
+# ╠═94a22398-cb45-40b9-8810-a564e58d7856

5and6 - Percolation.jl

@@ -1,5 +1,5 @@
 ### A Pluto.jl notebook ###
-# v0.19.25
+# v0.19.27
 
 using Markdown
 using InteractiveUtils
@@ -36,7 +36,7 @@ In percolation theory, we have a *critical probability*, $p_c$ which is for $p <
 """
 
 # ╔═╡ 8aa6eaee-9238-4e74-bffc-606f08562ea4
-pl₁ = simshow(repeat((sample(1:-1:0, weights([0.75, 1-0.75]), (100,100))), inner = (10, 10)))
+pl₁ = simshow(repeat((sample(1:-1:0, weights([0.6, 1-0.6]), (100,100))), inner = (10, 10)))
 
 # ╔═╡ ea1f7206-eea0-4014-a4fb-3c5f5e78660e
 md""" p= $(@bind p NumberField(0.01:0.01:1, default = 0.5))"""

7 and 8 - Random Walks.jl

@@ -147,8 +147,16 @@ end
 "Returns a two dimentional Levy flight."
 function levy_flight(N)
 	α = rand( (0:0.01:(2*π)), N)
-	r = [cdf_levy(rand(), 1.5) for i in 1:N]
+	r = []
 
+	p = .95
+	for i in 1:N
+		if rand()>p
+			push!(r, rand( (5:0.5:6) ))
+		else
+			push!(r, rand( (0.1:0.1:1.0) ))
+		end
+	end
 	xs = r .* cos.(α)
 	ys = r .* sin.(α)
 
@@ -1224,12 +1232,12 @@ version = "1.4.1+0"
 # ╔═╡ Cell order:
 # ╟─50b71a10-26d0-11ee-15e0-1b9fb9742c6c
 # ╠═0bdb9051-3b5f-4ede-8b61-4bbe07b30b5a
+# ╟─33a61359-0eaf-41d8-a7c4-bbc5bfa3e394
 # ╟─dbe07cd8-87f4-463f-8b85-5edb1c9c2447
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 # ╠═164c1ec3-0970-414d-9826-ac8833b55c28
 # ╟─9f7e87d7-2197-421b-97e1-8e183fb9c003
 # ╟─e7de8942-df19-45a3-a8f6-18b900c8453c
-# ╟─33a61359-0eaf-41d8-a7c4-bbc5bfa3e394
 # ╠═9d411317-cda3-4954-b5df-fab5fc2c95f9
 # ╟─fdcf6325-464a-4a84-8218-6156b76c49bd
 # ╟─0595936a-34a3-48fb-9acb-1786d8bbf810