diff --git a/README.md b/README.md
new file mode 100644
index 0000000000000000000000000000000000000000..ad0d5a1914fa8ca96ce1151091d2667cd63fef4d
--- /dev/null
+++ b/README.md
@@ -0,0 +1,15 @@
+# Estimating pi (π) with Monte Carlo.
+This is for the Uebung.
+
+    go build .
+
+Is all one needs.
+
+Cross compiling for windows...
+
+   GOOS=windows GOARCH=amd64 go build .
+   
+# BUGS
+
+There have been some terrible bugs in gonum/plot - mostly to do with large numbers of points. I am not going to fix them. Since seeing this, I have swapped to using a different chart package.
+
diff --git a/go.mod b/go.mod
index cafdfab28e6a9978d65abd40ee9aa630440d2f4d..683fe552e9b2f507643989fb641c2b4dd457a0f6 100644
--- a/go.mod
+++ b/go.mod
@@ -2,4 +2,4 @@ module pi
 
 go 1.16
 
-require gonum.org/v1/plot v0.11.0
+require gonum.org/v1/plot v0.12.0
diff --git a/go.sum b/go.sum
index ee0a7c868ff0301d3689f45f1718243ca1892220..6cc5185459fdc5721e3d9d1eefa4fd4334a0931d 100644
--- a/go.sum
+++ b/go.sum
@@ -1,4 +1,5 @@
 dmitri.shuralyov.com/gpu/mtl v0.0.0-20190408044501-666a987793e9/go.mod h1:H6x//7gZCb22OMCxBHrMx7a5I7Hp++hsVxbQ4BYO7hU=
+dmitri.shuralyov.com/gpu/mtl v0.0.0-20201218220906-28db891af037/go.mod h1:H6x//7gZCb22OMCxBHrMx7a5I7Hp++hsVxbQ4BYO7hU=
 gioui.org v0.0.0-20210308172011-57750fc8a0a6/go.mod h1:RSH6KIUZ0p2xy5zHDxgAM4zumjgTw83q2ge/PI+yyw8=
 git.sr.ht/~sbinet/gg v0.3.1 h1:LNhjNn8DerC8f9DHLz6lS0YYul/b602DUxDgGkd/Aik=
 git.sr.ht/~sbinet/gg v0.3.1/go.mod h1:KGYtlADtqsqANL9ueOFkWymvzUvLMQllU5Ixo+8v3pc=
@@ -23,6 +24,7 @@ github.com/go-fonts/liberation v0.2.0 h1:jAkAWJP4S+OsrPLZM4/eC9iW7CtHy+HBXrEwZXW
 github.com/go-fonts/liberation v0.2.0/go.mod h1:K6qoJYypsmfVjWg8KOVDQhLc8UDgIK2HYqyqAO9z7GY=
 github.com/go-fonts/stix v0.1.0/go.mod h1:w/c1f0ldAUlJmLBvlbkvVXLAD+tAMqobIIQpmnUIzUY=
 github.com/go-gl/glfw v0.0.0-20190409004039-e6da0acd62b1/go.mod h1:vR7hzQXu2zJy9AVAgeJqvqgH9Q5CA+iKCZ2gyEVpxRU=
+github.com/go-gl/glfw/v3.3/glfw v0.0.0-20200222043503-6f7a984d4dc4/go.mod h1:tQ2UAYgL5IevRw8kRxooKSPJfGvJ9fJQFa0TUsXzTg8=
 github.com/go-latex/latex v0.0.0-20210118124228-b3d85cf34e07/go.mod h1:CO1AlKB2CSIqUrmQPqA0gdRIlnLEY0gK5JGjh37zN5U=
 github.com/go-latex/latex v0.0.0-20210823091927-c0d11ff05a81 h1:6zl3BbBhdnMkpSj2YY30qV3gDcVBGtFgVsV3+/i+mKQ=
 github.com/go-latex/latex v0.0.0-20210823091927-c0d11ff05a81/go.mod h1:SX0U8uGpxhq9o2S/CELCSUxEWWAuoCUcVCQWv7G2OCk=
@@ -32,6 +34,8 @@ github.com/go-pdf/fpdf v0.6.0/go.mod h1:HzcnA+A23uwogo0tp9yU+l3V+KXhiESpt1PMayhO
 github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0 h1:DACJavvAHhabrF08vX0COfcOBJRhZ8lUbR+ZWIs0Y5g=
 github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0/go.mod h1:E/TSTwGwJL78qG/PmXZO1EjYhfJinVAhrmmHX6Z8B9k=
 github.com/google/go-cmp v0.5.7/go.mod h1:n+brtR0CgQNWTVd5ZUFpTBC8YFBDLK/h/bpaJ8/DtOE=
+github.com/google/go-cmp v0.5.8/go.mod h1:17dUlkBOakJ0+DkrSSNjCkIjxS6bF9zb3elmeNGIjoY=
+github.com/jezek/xgb v1.0.0/go.mod h1:nrhwO0FX/enq75I7Y7G8iN1ubpSGZEiA3v9e9GyRFlk=
 github.com/jung-kurt/gofpdf v1.0.0/go.mod h1:7Id9E/uU8ce6rXgefFLlgrJj/GYY22cpxn+r32jIOes=
 github.com/jung-kurt/gofpdf v1.0.3-0.20190309125859-24315acbbda5/go.mod h1:7Id9E/uU8ce6rXgefFLlgrJj/GYY22cpxn+r32jIOes=
 github.com/kisielk/gotool v1.0.0/go.mod h1:XhKaO+MFFWcvkIS/tQcRk01m1F5IRFswLeQ+oQHNcck=
@@ -46,16 +50,21 @@ github.com/ruudk/golang-pdf417 v0.0.0-20201230142125-a7e3863a1245/go.mod h1:pQAZ
 github.com/stretchr/testify v1.2.2/go.mod h1:a8OnRcib4nhh0OaRAV+Yts87kKdq0PP7pXfy6kDkUVs=
 github.com/yuin/goldmark v1.2.1/go.mod h1:3hX8gzYuyVAZsxl0MRgGTJEmQBFcNTphYh9decYSb74=
 github.com/yuin/goldmark v1.4.1/go.mod h1:mwnBkeHKe2W/ZEtQ+71ViKU8L12m81fl3OWwC1Zlc8k=
+github.com/yuin/goldmark v1.4.13/go.mod h1:6yULJ656Px+3vBD8DxQVa3kxgyrAnzto9xy5taEt/CY=
 golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
 golang.org/x/crypto v0.0.0-20190510104115-cbcb75029529/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI=
 golang.org/x/crypto v0.0.0-20191011191535-87dc89f01550/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI=
 golang.org/x/crypto v0.0.0-20200622213623-75b288015ac9/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto=
+golang.org/x/crypto v0.0.0-20210921155107-089bfa567519/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc=
 golang.org/x/exp v0.0.0-20180321215751-8460e604b9de/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
 golang.org/x/exp v0.0.0-20180807140117-3d87b88a115f/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
 golang.org/x/exp v0.0.0-20190125153040-c74c464bbbf2/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
 golang.org/x/exp v0.0.0-20190306152737-a1d7652674e8/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
-golang.org/x/exp v0.0.0-20191002040644-a1355ae1e2c3 h1:n9HxLrNxWWtEb1cA950nuEEj3QnKbtsCJ6KjcgisNUs=
+golang.org/x/exp v0.0.0-20190731235908-ec7cb31e5a56/go.mod h1:JhuoJpWY28nO4Vef9tZUw9qufEGTyX1+7lmHxV5q5G4=
 golang.org/x/exp v0.0.0-20191002040644-a1355ae1e2c3/go.mod h1:NOZ3BPKG0ec/BKJQgnvsSFpcKLM5xXVWnvZS97DWHgE=
+golang.org/x/exp v0.0.0-20220827204233-334a2380cb91 h1:tnebWN09GYg9OLPss1KXj8txwZc6X6uMr6VFdcGNbHw=
+golang.org/x/exp v0.0.0-20220827204233-334a2380cb91/go.mod h1:cyybsKvd6eL0RnXn6p/Grxp8F5bW7iYuBgsNCOHpMYE=
+golang.org/x/exp/shiny v0.0.0-20220722155223-a9213eeb770e/go.mod h1:VjAR7z0ngyATZTELrBSkxOOHhhlnVUxDye4mcjx5h/8=
 golang.org/x/image v0.0.0-20180708004352-c73c2afc3b81/go.mod h1:ux5Hcp/YLpHSI86hEcLt0YII63i6oz57MZXIpbrjZUs=
 golang.org/x/image v0.0.0-20190227222117-0694c2d4d067/go.mod h1:kZ7UVZpmo3dzQBMxlp+ypCbDeSB+sBbTgSJuh5dn5js=
 golang.org/x/image v0.0.0-20190802002840-cff245a6509b/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
@@ -68,19 +77,29 @@ golang.org/x/image v0.0.0-20210216034530-4410531fe030/go.mod h1:FeLwcggjj3mMvU+o
 golang.org/x/image v0.0.0-20210607152325-775e3b0c77b9/go.mod h1:023OzeP/+EPmXeapQh35lcL3II3LrY8Ic+EFFKVhULM=
 golang.org/x/image v0.0.0-20210628002857-a66eb6448b8d/go.mod h1:023OzeP/+EPmXeapQh35lcL3II3LrY8Ic+EFFKVhULM=
 golang.org/x/image v0.0.0-20211028202545-6944b10bf410/go.mod h1:023OzeP/+EPmXeapQh35lcL3II3LrY8Ic+EFFKVhULM=
-golang.org/x/image v0.0.0-20220302094943-723b81ca9867 h1:TcHcE0vrmgzNH1v3ppjcMGbhG5+9fMuvOmUYwNEF4q4=
 golang.org/x/image v0.0.0-20220302094943-723b81ca9867/go.mod h1:023OzeP/+EPmXeapQh35lcL3II3LrY8Ic+EFFKVhULM=
+golang.org/x/image v0.0.0-20220902085622-e7cb96979f69 h1:Lj6HJGCSn5AjxRAH2+r35Mir4icalbqku+CLUtjnvXY=
+golang.org/x/image v0.0.0-20220902085622-e7cb96979f69/go.mod h1:doUCurBvlfPMKfmIpRIywoHmhN3VyhnoFDbvIEWF4hY=
+golang.org/x/mobile v0.0.0-20190312151609-d3739f865fa6/go.mod h1:z+o9i4GpDbdi3rU15maQ/Ox0txvL9dWGYEHz965HBQE=
 golang.org/x/mobile v0.0.0-20190719004257-d2bd2a29d028/go.mod h1:E/iHnbuqvinMTCcRqshq8CkpyQDoeVncDDYHnLhea+o=
+golang.org/x/mobile v0.0.0-20201217150744-e6ae53a27f4f/go.mod h1:skQtrUTUwhdJvXM/2KKJzY8pDgNr9I/FOMqDVRPBUS4=
 golang.org/x/mod v0.1.0/go.mod h1:0QHyrYULN0/3qlju5TqG8bIK38QM8yzMo5ekMj3DlcY=
+golang.org/x/mod v0.1.1-0.20191105210325-c90efee705ee/go.mod h1:QqPTAvyqsEbceGzBzNggFXnrqF1CaUcvgkdR5Ot7KZg=
+golang.org/x/mod v0.1.1-0.20191209134235-331c550502dd/go.mod h1:s0Qsj1ACt9ePp/hMypM3fl4fZqREWJwdYDEqhRiZZUA=
 golang.org/x/mod v0.3.0/go.mod h1:s0Qsj1ACt9ePp/hMypM3fl4fZqREWJwdYDEqhRiZZUA=
 golang.org/x/mod v0.5.1/go.mod h1:5OXOZSfqPIIbmVBIIKWRFfZjPR0E5r58TLhUjH0a2Ro=
+golang.org/x/mod v0.6.0-dev.0.20220419223038-86c51ed26bb4/go.mod h1:jJ57K6gSWd91VN4djpZkiMVwK6gcyfeH4XE8wZrZaV4=
+golang.org/x/net v0.0.0-20190311183353-d8887717615a/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
 golang.org/x/net v0.0.0-20190404232315-eb5bcb51f2a3/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
 golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s=
 golang.org/x/net v0.0.0-20201021035429-f5854403a974/go.mod h1:sp8m0HH+o8qH0wwXwYZr8TS3Oi6o0r6Gce1SSxlDquU=
+golang.org/x/net v0.0.0-20210226172049-e18ecbb05110/go.mod h1:m0MpNAwzfU5UDzcl9v0D8zg8gWTRqZa9RBIspLL5mdg=
 golang.org/x/net v0.0.0-20211015210444-4f30a5c0130f/go.mod h1:9nx3DQGgdP8bBQD5qxJ1jj9UTztislL4KSBs9R2vV5Y=
+golang.org/x/net v0.0.0-20220722155237-a158d28d115b/go.mod h1:XRhObCWvk6IyKnWLug+ECip1KBveYUHfp+8e9klMJ9c=
 golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sync v0.0.0-20201020160332-67f06af15bc9/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sync v0.0.0-20210220032951-036812b2e83c/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
+golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
 golang.org/x/sys v0.0.0-20190312061237-fead79001313/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
 golang.org/x/sys v0.0.0-20190412213103-97732733099d/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
@@ -89,8 +108,12 @@ golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7w
 golang.org/x/sys v0.0.0-20210119212857-b64e53b001e4/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
 golang.org/x/sys v0.0.0-20210304124612-50617c2ba197/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
 golang.org/x/sys v0.0.0-20210423082822-04245dca01da/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
 golang.org/x/sys v0.0.0-20211019181941-9d821ace8654/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+golang.org/x/sys v0.0.0-20220520151302-bc2c85ada10a/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+golang.org/x/sys v0.0.0-20220722155257-8c9f86f7a55f/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
 golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo=
+golang.org/x/term v0.0.0-20210927222741-03fcf44c2211/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8=
 golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
 golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
 golang.org/x/text v0.3.5/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
@@ -100,10 +123,13 @@ golang.org/x/text v0.3.7/go.mod h1:u+2+/6zg+i71rQMx5EYifcz6MCKuco9NR6JIITiCfzQ=
 golang.org/x/tools v0.0.0-20180525024113-a5b4c53f6e8b/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
 golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
 golang.org/x/tools v0.0.0-20190206041539-40960b6deb8e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
+golang.org/x/tools v0.0.0-20190312151545-0bb0c0a6e846/go.mod h1:LCzVGOaR6xXOjkQ3onu1FJEFr0SW1gC7cKk1uF8kGRs=
 golang.org/x/tools v0.0.0-20190927191325-030b2cf1153e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo=
 golang.org/x/tools v0.0.0-20191119224855-298f0cb1881e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo=
+golang.org/x/tools v0.0.0-20200117012304-6edc0a871e69/go.mod h1:TB2adYChydJhpapKDTa4BR/hXlZSLoq2Wpct/0txZ28=
 golang.org/x/tools v0.1.0/go.mod h1:xkSsbof2nBLbhDlRMhhhyNLN/zl3eTqcnHD5viDpcZ0=
 golang.org/x/tools v0.1.9/go.mod h1:nABZi5QlRsZVlzPpHl034qft6wpY4eDcsTt5AaioBiU=
+golang.org/x/tools v0.1.12/go.mod h1:hNGJHUnrk76NpqgfD5Aqm5Crs+Hm0VOH/i9J2+nxYbc=
 golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
 golang.org/x/xerrors v0.0.0-20191011141410-1b5146add898/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
 golang.org/x/xerrors v0.0.0-20191204190536-9bdfabe68543/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
@@ -111,14 +137,14 @@ golang.org/x/xerrors v0.0.0-20200804184101-5ec99f83aff1/go.mod h1:I/5z698sn9Ka8T
 gonum.org/v1/gonum v0.0.0-20180816165407-929014505bf4/go.mod h1:Y+Yx5eoAFn32cQvJDxZx5Dpnq+c3wtXuadVZAcxbbBo=
 gonum.org/v1/gonum v0.8.2/go.mod h1:oe/vMfY3deqTw+1EZJhuvEW2iwGF1bW9wwu7XCu0+v0=
 gonum.org/v1/gonum v0.9.3/go.mod h1:TZumC3NeyVQskjXqmyWt4S3bINhy7B4eYwW69EbyX+0=
-gonum.org/v1/gonum v0.11.0 h1:f1IJhK4Km5tBJmaiJXtk/PkL4cdVX6J+tGiM187uT5E=
-gonum.org/v1/gonum v0.11.0/go.mod h1:fSG4YDCxxUZQJ7rKsQrj0gMOg00Il0Z96/qMA4bVQhA=
+gonum.org/v1/gonum v0.12.0 h1:xKuo6hzt+gMav00meVPUlXwSdoEJP46BR+wdxQEFK2o=
+gonum.org/v1/gonum v0.12.0/go.mod h1:73TDxJfAAHeA8Mk9mf8NlIppyhQNo5GLTcYeqgo2lvY=
 gonum.org/v1/netlib v0.0.0-20190313105609-8cb42192e0e0/go.mod h1:wa6Ws7BG/ESfp6dHfk7C6KdzKA7wR7u/rKwOGE66zvw=
 gonum.org/v1/plot v0.0.0-20190515093506-e2840ee46a6b/go.mod h1:Wt8AAjI+ypCyYX3nZBvf6cAIx93T+c/OS2HFAYskSZc=
 gonum.org/v1/plot v0.9.0/go.mod h1:3Pcqqmp6RHvJI72kgb8fThyUnav364FOsdDo2aGW5lY=
 gonum.org/v1/plot v0.10.1/go.mod h1:VZW5OlhkL1mysU9vaqNHnsy86inf6Ot+jB3r+BczCEo=
-gonum.org/v1/plot v0.11.0 h1:z2ZkgNqW34d0oYUzd80RRlc0L9kWtenqK4kflZG1lGc=
-gonum.org/v1/plot v0.11.0/go.mod h1:fH9YnKnDKax0u5EzHVXvhN5HJwtMFWIOLNuhgUahbCQ=
+gonum.org/v1/plot v0.12.0 h1:y1ZNmfz/xHuHvtgFe8USZVyykQo5ERXPnspQNVK15Og=
+gonum.org/v1/plot v0.12.0/go.mod h1:PgiMf9+3A3PnZdJIciIXmyN1FwdAA6rXELSN761oQkw=
 honnef.co/go/tools v0.1.3/go.mod h1:NgwopIslSNH47DimFoV78dnkksY2EFtX0ajyb3K/las=
 rsc.io/pdf v0.1.1 h1:k1MczvYDUvJBe93bYd7wrZLLUEcLZAuF824/I4e5Xr4=
 rsc.io/pdf v0.1.1/go.mod h1:n8OzWcQ6Sp37PL01nO98y4iUCRdTGarVfzxY20ICaU4=