diff --git a/go.mod b/go.mod
index c1180c3..d89b35d 100644
--- a/go.mod
+++ b/go.mod
@@ -7,9 +7,9 @@ toolchain go1.21.6
 require (
 	github.com/gopxl/pixel/v2 v2.1.0
 	github.com/mazznoer/colorgrad v0.9.1
-	github.com/mlange-42/arche v0.12.0
-	github.com/mlange-42/arche-model v0.7.0
-	github.com/stretchr/testify v1.8.4
+	github.com/mlange-42/arche v0.13.0
+	github.com/mlange-42/arche-model v0.9.0
+	github.com/stretchr/testify v1.9.0
 	golang.org/x/image v0.15.0
 	gonum.org/v1/plot v0.14.0
 )
diff --git a/go.sum b/go.sum
index fe4d14d..dbfc579 100644
--- a/go.sum
+++ b/go.sum
@@ -42,16 +42,16 @@ github.com/mazznoer/colorgrad v0.9.1 h1:MB80JYVndKWSMEM1beNqnuOowWGhoQc3DXWXkFp6
 github.com/mazznoer/colorgrad v0.9.1/go.mod h1:WX2R9wt9B47+txJZVVpM9LY+LAGIdi4lTI5wIyreDH4=
 github.com/mazznoer/csscolorparser v0.1.2 h1:/UBHuQg792ePmGFzTQAC9u+XbFr7/HzP/Gj70Phyz2A=
 github.com/mazznoer/csscolorparser v0.1.2/go.mod h1:Aj22+L/rYN/Y6bj3bYqO3N6g1dtdHtGfQ32xZ5PJQic=
-github.com/mlange-42/arche v0.12.0 h1:qGrTcUlmo8Ad95x3k058a65UKxN/+GDCQlD1UMU3Xrw=
-github.com/mlange-42/arche v0.12.0/go.mod h1:gJ5J8vBreqrf4TcBomBFPGnWdE5P3qa4LtxYHn1gDcg=
-github.com/mlange-42/arche-model v0.7.0 h1:l8hcZXpENZBBGyrE5Ndczg7PXkvyzPlAGQ0iTjBziB4=
-github.com/mlange-42/arche-model v0.7.0/go.mod h1:Di0S5w5ljyZbD4NmcYV7otZ52mm+X71j35VKkf4FC/A=
+github.com/mlange-42/arche v0.13.0 h1:ef0fu9qC2KIr8wIlVs+CgeQ5CSUJ8A1Hut6nXYdf+xk=
+github.com/mlange-42/arche v0.13.0/go.mod h1:bFktKnvGDj2kP01xar79z0hKwGHdnoaEZR8HWmJkIyU=
+github.com/mlange-42/arche-model v0.9.0 h1:S/qIvZNra782+nPixPkV5Ay9lAO51T1Zy7y4J62p1lo=
+github.com/mlange-42/arche-model v0.9.0/go.mod h1:unGJaXLPdDUwMoPGKlTCW8HaRFVIRFILLHSWFp/DVY4=
 github.com/pkg/errors v0.9.1 h1:FEBLx1zS214owpjy7qsBeixbURkuhQAwrK5UwLGTwt4=
 github.com/pkg/errors v0.9.1/go.mod h1:bwawxfHBFNV+L2hUp1rHADufV3IMtnDRdf1r5NINEl0=
 github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZbAQM=
 github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4=
-github.com/stretchr/testify v1.8.4 h1:CcVxjf3Q8PM0mHUKJCdn+eZZtm5yQwehR5yeSVQQcUk=
-github.com/stretchr/testify v1.8.4/go.mod h1:sz/lmYIOXD/1dqDmKjjqLyZ2RngseejIcXlSw2iwfAo=
+github.com/stretchr/testify v1.9.0 h1:HtqpIVDClZ4nwg75+f6Lvsy/wHu+3BoSGCbBAcpTsTg=
+github.com/stretchr/testify v1.9.0/go.mod h1:r2ic/lqez/lEtzL7wO/rwa5dbSLXVDPFyf8C91i36aY=
 github.com/yuin/goldmark v1.2.1/go.mod h1:3hX8gzYuyVAZsxl0MRgGTJEmQBFcNTphYh9decYSb74=
 golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
 golang.org/x/crypto v0.0.0-20191011191535-87dc89f01550/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI=