diff --git a/Project.toml b/Project.toml
index 0cc7316e..005e6f49 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "SparseConnectivityTracer"
 uuid = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
 authors = ["Adrian Hill <gh@adrianhill.de>"]
-version = "0.1.0"
+version = "0.2.0-DEV"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/README.md b/README.md
index 00bb1d25..8a0117a1 100644
--- a/README.md
+++ b/README.md
@@ -8,8 +8,7 @@
 
 Fast sparsity detection via operator-overloading.
 
-Will soon include Jacobian sparsity detection ([#19](https://github.com/adrhill/SparseConnectivityTracer.jl/issues/19))
-and Hessian sparsity detection ([#20](https://github.com/adrhill/SparseConnectivityTracer.jl/issues/20)).
+Will soon include Hessian sparsity detection ([#20](https://github.com/adrhill/SparseConnectivityTracer.jl/issues/20)).
 
 ## Installation 
 To install this package, open the Julia REPL and run 
@@ -26,7 +25,7 @@ julia> x = rand(3);
 
 julia> f(x) = [x[1]^2, 2 * x[1] * x[2]^2, sin(x[3])];
 
-julia> connectivity(f, x)
+julia> pattern(f, JacobianTracer, x)
 3×3 SparseArrays.SparseMatrixCSC{Bool, UInt64} with 4 stored entries:
  1  ⋅  ⋅
  1  1  ⋅
@@ -41,37 +40,32 @@ julia> x = rand(28, 28, 3, 1);
 
 julia> layer = Conv((3, 3), 3 => 8);
 
-julia> connectivity(layer, x)
+julia> pattern(layer, JacobianTracer, x)
 5408×2352 SparseArrays.SparseMatrixCSC{Bool, UInt64} with 146016 stored entries:
-⎡⠙⢶⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⎤
-⎢⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⎥
-⎢⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠉⠳⣦⡀⎥
-⎢⠙⢷⣄⠀⠀⠀⠉⠻⣦⡀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠈⠁⎥
-⎢⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠉⠳⣦⡀⠀⠀⎥
-⎢⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠈⠻⣦⡀⎥
-⎢⠙⢷⣄⠀⠀⠀⠉⠻⣦⡀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠈⠁⎥
-⎢⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠈⠻⣦⡀⠀⠀⎥
-⎢⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠈⠻⣦⡀⎥
-⎢⠙⢷⣄⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠈⠁⎥
-⎢⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠈⠻⣦⡀⠀⠀⎥
-⎢⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⎥
-⎢⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⎥
-⎢⠀⠀⠙⢷⣄⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⎥
-⎢⣀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠈⠻⣦⡀⎥
-⎢⠙⢷⣄⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⎥
-⎢⠀⠀⠙⢷⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⎥
-⎢⣀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠈⠻⣦⡀⎥
-⎢⠙⢷⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⎥
-⎢⠀⠀⠙⠷⣄⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⎥
-⎢⣀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠈⠻⣦⡀⎥
-⎢⠙⠷⣄⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⎥
-⎢⠀⠀⠈⠻⣦⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⣦⡀⠀⠀⎥
-⎣⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠻⢦⡀⎦
+⎡⠙⢦⡀⠀⠀⠘⢷⣄⠀⠀⠈⠻⣦⡀⠀⠀⠀⎤
+⎢⠀⠀⠙⢷⣄⠀⠀⠙⠷⣄⠀⠀⠈⠻⣦⡀⠀⎥
+⎢⢶⣄⠀⠀⠙⠳⣦⡀⠀⠈⠳⢦⡀⠀⠈⠛⠂⎥
+⎢⠀⠙⢷⣄⠀⠀⠈⠻⣦⡀⠀⠀⠙⢦⣄⠀⠀⎥
+⎢⣀⡀⠀⠉⠳⣄⡀⠀⠈⠻⣦⣀⠀⠀⠙⢷⡄⎥
+⎢⠈⠻⣦⡀⠀⠈⠛⢦⡀⠀⠀⠙⢷⣄⠀⠀⠀⎥
+⎢⠀⠀⠈⠻⣦⡀⠀⠀⠙⢷⣄⠀⠀⠙⠷⣄⠀⎥
+⎢⠻⣦⡀⠀⠈⠙⢷⣄⠀⠀⠉⠻⣦⡀⠀⠈⠁⎥
+⎢⠀⠀⠙⢦⣀⠀⠀⠙⢷⣄⠀⠀⠈⠻⣦⡀⠀⎥
+⎢⢤⣄⠀⠀⠙⠳⣄⡀⠀⠉⠳⣤⡀⠀⠈⠛⠂⎥
+⎢⠀⠙⢷⣄⠀⠀⠈⠻⣦⡀⠀⠈⠙⢦⡀⠀⠀⎥
+⎢⣀⠀⠀⠙⢷⣄⡀⠀⠈⠻⣦⣀⠀⠀⠙⢷⡄⎥
+⎢⠈⠳⣦⡀⠀⠈⠻⣦⡀⠀⠀⠙⢷⣄⠀⠀⠀⎥
+⎢⠀⠀⠈⠻⣦⡀⠀⠀⠙⢦⣄⠀⠀⠙⢷⣄⠀⎥
+⎢⠻⣦⡀⠀⠈⠙⢷⣄⠀⠀⠉⠳⣄⡀⠀⠉⠁⎥
+⎢⠀⠈⠛⢦⡀⠀⠀⠙⢷⣄⠀⠀⠈⠻⣦⡀⠀⎥
+⎢⢤⣄⠀⠀⠙⠶⣄⠀⠀⠙⠷⣤⡀⠀⠈⠻⠆⎥
+⎢⠀⠙⢷⣄⠀⠀⠈⠳⣦⡀⠀⠈⠻⣦⡀⠀⠀⎥
+⎣⠀⠀⠀⠙⢷⣄⠀⠀⠈⠻⣦⠀⠀⠀⠙⢦⡀⎦
 ```
 
-SparseConnectivityTracer enumerates inputs `x` and primal outputs `y=f(x)` and returns a sparse connectivity matrix `C` of size $m \times n$, where `C[i, j]` is `true` if the compute graph connects the $j$-th entry in `x` to the $i$-th entry in `y`.
+SparseConnectivityTracer enumerates inputs `x` and primal outputs `y = f(x)` and returns a sparse matrix `C` of size $m \times n$, where `C[i, j]` is `true` if the compute graph connects the $j$-th entry in `x` to the $i$-th entry in `y`.
 
-For more detailled examples, take a look at the [API reference](https://adrianhill.de/SparseConnectivityTracer.jl/dev/api).
+For more detailled examples, take a look at the [documentation](https://adrianhill.de/SparseConnectivityTracer.jl/dev).
 
 ## Related packages
 * [SparseDiffTools.jl](https://github.com/JuliaDiff/SparseDiffTools.jl): automatic sparsity detection via Symbolics.jl and Cassette.jl
diff --git a/docs/src/api.md b/docs/src/api.md
index baac9133..d3e6c2a4 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -10,19 +10,26 @@ CollapsedDocStrings = true
 
 ## Interface
 ```@docs
-connectivity
+pattern
 TracerSparsityDetector
 ```
 
 ## Internals
-SparseConnectivityTracer works by pushing a `Number` type called [`Tracer`](@ref) through generic functions:
+SparseConnectivityTracer works by pushing `Number` types called tracers through generic functions.
+Currently, two tracer types are provided:
+
+```@docs
+JacobianTracer
+ConnectivityTracer
+```
+
+Utilities to create tracers:
 ```@docs
-Tracer
 tracer
 trace_input
 ```
 
-The following utilities can be used to extract input indices from [`Tracer`](@ref)s:
+Utility to extract input indices from tracers:
 ```@docs
 inputs
 ```
diff --git a/src/SparseConnectivityTracer.jl b/src/SparseConnectivityTracer.jl
index e84fac90..039d9896 100644
--- a/src/SparseConnectivityTracer.jl
+++ b/src/SparseConnectivityTracer.jl
@@ -4,17 +4,20 @@ using ADTypes: ADTypes
 import Random: rand, AbstractRNG, SamplerType
 import SparseArrays: sparse
 
-include("tracer.jl")
+abstract type AbstractTracer <: Number end
+
+include("tracers.jl")
 include("conversion.jl")
 include("operators.jl")
-include("overload_tracer.jl")
-include("connectivity.jl")
+include("overload_connectivity.jl")
+include("overload_jacobian.jl")
+include("pattern.jl")
 include("adtypes.jl")
 
-export Tracer
+export JacobianTracer, ConnectivityTracer
 export tracer, trace_input
 export inputs
-export connectivity
+export pattern
 export TracerSparsityDetector
 
 end # module
diff --git a/src/adtypes.jl b/src/adtypes.jl
index eabea79a..25a39ea4 100644
--- a/src/adtypes.jl
+++ b/src/adtypes.jl
@@ -18,13 +18,14 @@ julia> ADTypes.jacobian_sparsity(diff, rand(4), TracerSparsityDetector())
 struct TracerSparsityDetector <: ADTypes.AbstractSparsityDetector end
 
 function ADTypes.jacobian_sparsity(f, x, ::TracerSparsityDetector)
-    return connectivity(f, x)
+    return pattern(f, JacobianTracer, x)
 end
 
 function ADTypes.jacobian_sparsity(f!, y, x, ::TracerSparsityDetector)
-    return connectivity(f!, y, x)
+    return pattern(f!, y, JacobianTracer, x)
 end
 
 function ADTypes.hessian_sparsity(f, x, ::TracerSparsityDetector)
+    # TODO: return pattern(f, HessianTracer, x)
     return error("Hessian sparsity is not yet implemented for `TracerSparsityDetector`.")
 end
diff --git a/src/connectivity.jl b/src/connectivity.jl
deleted file mode 100644
index fd736017..00000000
--- a/src/connectivity.jl
+++ /dev/null
@@ -1,98 +0,0 @@
-## Enumerate inputs
-
-"""
-    trace_input(x)
-
-Enumerates input indices and constructs [`Tracer`](@ref)s.
-
-## Example
-```jldoctest
-julia> x = rand(3);
-
-julia> f(x) = [x[1]^2, 2 * x[1] * x[2]^2, sin(x[3])];
-
-julia> xt = trace_input(x)
-3-element Vector{Tracer}:
- Tracer(1,)
- Tracer(2,)
- Tracer(3,)
-
-julia> yt = f(xt)
-3-element Vector{Tracer}:
-   Tracer(1,)
- Tracer(1, 2)
-   Tracer(3,)
-```
-"""
-trace_input(x) = trace_input(x, 1)
-trace_input(::Number, i) = tracer(i)
-function trace_input(x::AbstractArray, i)
-    indices = (i - 1) .+ reshape(1:length(x), size(x))
-    return tracer.(indices)
-end
-
-## Construct connectivity matrix
-"""
-    connectivity(f, x)
-
-Enumerates inputs `x` and primal outputs `y=f(x)` and returns sparse connectivity matrix `C` of size `(m, n)`
-where `C[i, j]` is true if the compute graph connects the `i`-th entry in `y` to the `j`-th entry in `x`.
-
-## Example
-```jldoctest
-julia> x = rand(3);
-
-julia> f(x) = [x[1]^2, 2 * x[1] * x[2]^2, sin(x[3])];
-
-julia> connectivity(f, x)
-3×3 SparseArrays.SparseMatrixCSC{Bool, UInt64} with 4 stored entries:
- 1  ⋅  ⋅
- 1  1  ⋅
- ⋅  ⋅  1
-```
-"""
-function connectivity(f, x)
-    xt = trace_input(x)
-    yt = f(xt)
-    return _connectivity(xt, yt)
-end
-
-"""
-    connectivity(f!, y, x)
-
-Enumerates inputs `x` and primal outputs `y` after `f!(y, x)` and returns sparse connectivity matrix `C` of size `(m, n)`
-where `C[i, j]` is true if the compute graph connects the `i`-th entry in `y` to the `j`-th entry in `x`.
-"""
-function connectivity(f!, y, x)
-    xt = trace_input(x)
-    yt = similar(y, Tracer)
-    f!(yt, xt)
-    return _connectivity(xt, yt)
-end
-
-_connectivity(xt::Tracer, yt::Number) = _connectivity([xt], [yt])
-_connectivity(xt::Tracer, yt::AbstractArray{Number}) = _connectivity([xt], yt)
-_connectivity(xt::AbstractArray{Tracer}, yt::Number) = _connectivity(xt, [yt])
-function _connectivity(xt::AbstractArray{Tracer}, yt::AbstractArray{<:Number})
-    return connectivity_sparsematrixcsc(xt, yt)
-end
-
-function connectivity_sparsematrixcsc(
-    xt::AbstractArray{Tracer}, yt::AbstractArray{<:Number}
-)
-    # Construct connectivity matrix of size (ouput_dim, input_dim)
-    n, m = length(xt), length(yt)
-    I = UInt64[]
-    J = UInt64[]
-    V = Bool[]
-    for (i, y) in enumerate(yt)
-        if y isa Tracer
-            for j in inputs(y)
-                push!(I, i)
-                push!(J, j)
-                push!(V, true)
-            end
-        end
-    end
-    return sparse(I, J, V, m, n)
-end
diff --git a/src/conversion.jl b/src/conversion.jl
index fad90eb4..fcdc5b0d 100644
--- a/src/conversion.jl
+++ b/src/conversion.jl
@@ -1,23 +1,25 @@
 ## Type conversions
-Base.promote_rule(::Type{Tracer}, ::Type{N}) where {N<:Number} = Tracer
-Base.promote_rule(::Type{N}, ::Type{Tracer}) where {N<:Number} = Tracer
+for T in (:JacobianTracer, :ConnectivityTracer)
+    @eval Base.promote_rule(::Type{$T}, ::Type{N}) where {N<:Number} = $T
+    @eval Base.promote_rule(::Type{N}, ::Type{$T}) where {N<:Number} = $T
 
-Base.big(::Type{Tracer})   = Tracer
-Base.widen(::Type{Tracer}) = Tracer
-Base.widen(t::Tracer)      = t
+    @eval Base.big(::Type{$T})   = $T
+    @eval Base.widen(::Type{$T}) = $T
+    @eval Base.widen(t::$T)      = t
 
-Base.convert(::Type{Tracer}, x::Number)   = EMPTY_TRACER
-Base.convert(::Type{Tracer}, t::Tracer)   = t
-Base.convert(::Type{<:Number}, t::Tracer) = t
+    @eval Base.convert(::Type{$T}, x::Number) = empty($T)
+    @eval Base.convert(::Type{$T}, t::$T) = t
+    @eval Base.convert(::Type{<:Number}, t::$T) = t
 
-## Array constructors
-Base.zero(::Type{Tracer}) = EMPTY_TRACER
-Base.one(::Type{Tracer})  = EMPTY_TRACER
+    ## Array constructors
+    @eval Base.zero(::Type{$T}) = empty($T)
+    @eval Base.one(::Type{$T})  = empty($T)
 
-Base.similar(a::Array{Tracer,1})                               = zeros(Tracer, size(a, 1))
-Base.similar(a::Array{Tracer,2})                               = zeros(Tracer, size(a, 1), size(a, 2))
-Base.similar(a::Array{T,1}, ::Type{Tracer}) where {T}          = zeros(Tracer, size(a, 1))
-Base.similar(a::Array{T,2}, ::Type{Tracer}) where {T}          = zeros(Tracer, size(a, 1), size(a, 2))
-Base.similar(::Array{Tracer}, m::Int)                          = zeros(Tracer, m)
-Base.similar(::Array, ::Type{Tracer}, dims::Dims{N}) where {N} = zeros(Tracer, dims)
-Base.similar(::Array{Tracer}, dims::Dims{N}) where {N}         = zeros(Tracer, dims)
+    @eval Base.similar(a::Array{$T,1})                               = zeros($T, size(a, 1))
+    @eval Base.similar(a::Array{$T,2})                               = zeros($T, size(a, 1), size(a, 2))
+    @eval Base.similar(a::Array{A,1}, ::Type{$T}) where {A}          = zeros($T, size(a, 1))
+    @eval Base.similar(a::Array{A,2}, ::Type{$T}) where {A}          = zeros($T, size(a, 1), size(a, 2))
+    @eval Base.similar(::Array{$T}, m::Int)                          = zeros($T, m)
+    @eval Base.similar(::Array, ::Type{$T}, dims::Dims{N}) where {N} = zeros($T, dims)
+    @eval Base.similar(::Array{$T}, dims::Dims{N}) where {N}         = zeros($T, dims)
+end
diff --git a/src/overload_connectivity.jl b/src/overload_connectivity.jl
new file mode 100644
index 00000000..2bd667b3
--- /dev/null
+++ b/src/overload_connectivity.jl
@@ -0,0 +1,32 @@
+for fn in union(ops_1_to_1_s, ops_1_to_1_f, ops_1_to_1_z)
+    @eval Base.$fn(t::ConnectivityTracer) = t
+end
+
+for fn in ops_1_to_1_const
+    @eval Base.$fn(::ConnectivityTracer) = EMPTY_CONNECTIVITY_TRACER
+end
+
+for fn in ops_1_to_2
+    @eval Base.$fn(t::ConnectivityTracer) = (t, t)
+end
+
+for fn in ops_2_to_1
+    @eval Base.$fn(a::ConnectivityTracer, b::ConnectivityTracer) = uniontracer(a, b)
+    @eval Base.$fn(t::ConnectivityTracer, ::Number) = t
+    @eval Base.$fn(::Number, t::ConnectivityTracer) = t
+end
+
+# Extra types required for exponent
+Base.:^(a::ConnectivityTracer, b::ConnectivityTracer) = uniontracer(a, b)
+for T in (:Real, :Integer, :Rational)
+    @eval Base.:^(t::ConnectivityTracer, ::$T) = t
+    @eval Base.:^(::$T, t::ConnectivityTracer) = t
+end
+Base.:^(t::ConnectivityTracer, ::Irrational{:ℯ}) = t
+Base.:^(::Irrational{:ℯ}, t::ConnectivityTracer) = t
+
+## Rounding
+Base.round(t::ConnectivityTracer, ::RoundingMode; kwargs...) = t
+
+## Random numbers
+rand(::AbstractRNG, ::SamplerType{ConnectivityTracer}) = EMPTY_CONNECTIVITY_TRACER
diff --git a/src/overload_jacobian.jl b/src/overload_jacobian.jl
new file mode 100644
index 00000000..6b4d9b15
--- /dev/null
+++ b/src/overload_jacobian.jl
@@ -0,0 +1,68 @@
+for fn in union(ops_1_to_1_s, ops_1_to_1_f)
+    @eval Base.$fn(t::JacobianTracer) = t
+end
+
+for fn in union(ops_1_to_1_z, ops_1_to_1_const)
+    @eval Base.$fn(::JacobianTracer) = EMPTY_JACOBIAN_TRACER
+end
+
+for fn in union(
+    ops_2_to_1_ssc,
+    ops_2_to_1_ssz,
+    ops_2_to_1_sfc,
+    ops_2_to_1_sfz,
+    ops_2_to_1_fsc,
+    ops_2_to_1_fsz,
+    ops_2_to_1_ffc,
+    ops_2_to_1_ffz,
+)
+    @eval Base.$fn(a::JacobianTracer, b::JacobianTracer) = uniontracer(a, b)
+    @eval Base.$fn(t::JacobianTracer, ::Number) = t
+    @eval Base.$fn(::Number, t::JacobianTracer) = t
+end
+
+for fn in union(ops_2_to_1_zsz, ops_2_to_1_zfz)
+    @eval Base.$fn(::JacobianTracer, t::JacobianTracer) = t
+    @eval Base.$fn(::JacobianTracer, ::Number) = EMPTY_JACOBIAN_TRACER
+    @eval Base.$fn(::Number, t::JacobianTracer) = t
+end
+for fn in union(ops_2_to_1_szz, ops_2_to_1_fzz)
+    @eval Base.$fn(t::JacobianTracer, ::JacobianTracer) = t
+    @eval Base.$fn(t::JacobianTracer, ::Number) = t
+    @eval Base.$fn(::Number, t::JacobianTracer) = EMPTY_JACOBIAN_TRACER
+end
+for fn in ops_2_to_1_zzz
+    @eval Base.$fn(::JacobianTracer, ::JacobianTracer) = EMPTY_JACOBIAN_TRACER
+    @eval Base.$fn(::JacobianTracer, ::Number) = EMPTY_JACOBIAN_TRACER
+    @eval Base.$fn(::Number, ::JacobianTracer) = EMPTY_JACOBIAN_TRACER
+end
+
+for fn in union(ops_1_to_2_ss, ops_1_to_2_sf, ops_1_to_2_fs, ops_1_to_2_ff)
+    @eval Base.$fn(t::JacobianTracer) = (t, t)
+end
+
+for fn in union(ops_1_to_2_sz, ops_1_to_2_fz)
+    @eval Base.$fn(t::JacobianTracer) = (t, EMPTY_JACOBIAN_TRACER)
+end
+
+for fn in union(ops_1_to_2_zs, ops_1_to_2_zf)
+    @eval Base.$fn(t::JacobianTracer) = (EMPTY_JACOBIAN_TRACER, t)
+end
+for fn in ops_1_to_2_zz
+    @eval Base.$fn(::JacobianTracer) = (EMPTY_JACOBIAN_TRACER, EMPTY_JACOBIAN_TRACER)
+end
+
+# Extra types required for exponent
+Base.:^(a::JacobianTracer, b::JacobianTracer) = uniontracer(a, b)
+for T in (:Real, :Integer, :Rational)
+    @eval Base.:^(t::JacobianTracer, ::$T) = t
+    @eval Base.:^(::$T, t::JacobianTracer) = t
+end
+Base.:^(t::JacobianTracer, ::Irrational{:ℯ}) = t
+Base.:^(::Irrational{:ℯ}, t::JacobianTracer) = t
+
+## Rounding
+Base.round(t::JacobianTracer, ::RoundingMode; kwargs...) = EMPTY_JACOBIAN_TRACER
+
+## Random numbers
+rand(::AbstractRNG, ::SamplerType{JacobianTracer}) = EMPTY_JACOBIAN_TRACER
diff --git a/src/overload_tracer.jl b/src/overload_tracer.jl
deleted file mode 100644
index 9409f715..00000000
--- a/src/overload_tracer.jl
+++ /dev/null
@@ -1,32 +0,0 @@
-for fn in union(ops_1_to_1_s, ops_1_to_1_f, ops_1_to_1_z)
-    @eval Base.$fn(t::Tracer) = t
-end
-
-for fn in ops_1_to_1_const
-    @eval Base.$fn(::Tracer) = EMPTY_TRACER
-end
-
-for fn in ops_1_to_2
-    @eval Base.$fn(t::Tracer) = (t, t)
-end
-
-for fn in ops_2_to_1
-    @eval Base.$fn(a::Tracer, b::Tracer) = uniontracer(a, b)
-    @eval Base.$fn(t::Tracer, ::Number) = t
-    @eval Base.$fn(::Number, t::Tracer) = t
-end
-
-# Extra types required for exponent
-Base.:^(a::Tracer, b::Tracer) = uniontracer(a, b)
-for T in (:Real, :Integer, :Rational)
-    @eval Base.:^(t::Tracer, ::$T) = t
-    @eval Base.:^(::$T, t::Tracer) = t
-end
-Base.:^(t::Tracer, ::Irrational{:ℯ}) = t
-Base.:^(::Irrational{:ℯ}, t::Tracer) = t
-
-## Rounding
-Base.round(t::Tracer, ::RoundingMode; kwargs...) = t
-
-## Random numbers
-rand(::AbstractRNG, ::SamplerType{Tracer}) = EMPTY_TRACER
diff --git a/src/pattern.jl b/src/pattern.jl
new file mode 100644
index 00000000..cde0afbe
--- /dev/null
+++ b/src/pattern.jl
@@ -0,0 +1,109 @@
+## Enumerate inputs
+
+"""
+    trace_input(JacobianTracer, x)
+    trace_input(ConnectivityTracer, x)
+
+
+Enumerates input indices and constructs the specified type of tracer.
+Supports [`JacobianTracer`](@ref) and [`ConnectivityTracer`](@ref).
+
+## Example
+```jldoctest
+julia> x = rand(3);
+
+julia> f(x) = [x[1]^2, 2 * x[1] * x[2]^2, sin(x[3])];
+
+julia> xt = trace_input(ConnectivityTracer, x)
+3-element Vector{ConnectivityTracer}:
+ ConnectivityTracer(1,)
+ ConnectivityTracer(2,)
+ ConnectivityTracer(3,)
+
+julia> yt = f(xt)
+3-element Vector{ConnectivityTracer}:
+   ConnectivityTracer(1,)
+ ConnectivityTracer(1, 2)
+   ConnectivityTracer(3,)
+```
+"""
+trace_input(::Type{T}, x) where {T<:AbstractTracer} = trace_input(T, x, 1)
+trace_input(::Type{T}, ::Number, i) where {T<:AbstractTracer} = tracer(T, i)
+function trace_input(::Type{T}, x::AbstractArray, i) where {T<:AbstractTracer}
+    indices = (i - 1) .+ reshape(1:length(x), size(x))
+    return tracer.(T, indices)
+end
+
+## Construct sparsity pattern matrix
+"""
+    pattern(f, JacobianTracer, x)
+
+Computes the sparsity pattern of the Jacobian of `y = f(x)`.
+
+    pattern(f, ConnectivityTracer, x)
+
+Enumerates inputs `x` and primal outputs `y = f(x)` and returns sparse matrix `C` of size `(m, n)`
+where `C[i, j]` is true if the compute graph connects the `i`-th entry in `y` to the `j`-th entry in `x`.
+
+## Example
+```jldoctest
+julia> x = rand(3);
+
+julia> f(x) = [x[1]^2, 2 * x[1] * x[2]^2, sin(x[3])];
+
+julia> pattern(f, ConnectivityTracer, x)
+3×3 SparseArrays.SparseMatrixCSC{Bool, UInt64} with 4 stored entries:
+ 1  ⋅  ⋅
+ 1  1  ⋅
+ ⋅  ⋅  1
+```
+"""
+function pattern(f, ::Type{T}, x) where {T<:AbstractTracer}
+    xt = trace_input(T, x)
+    yt = f(xt)
+    return _pattern(xt, yt)
+end
+
+"""
+    pattern(f!, y, JacobianTracer, x)
+
+Computes the sparsity pattern of the Jacobian of `f!(y, x)`.
+
+    pattern(f!, y, ConnectivityTracer, x)
+
+Enumerates inputs `x` and primal outputs `y` after `f!(y, x)` and returns sparse matrix `C` of size `(m, n)`
+where `C[i, j]` is true if the compute graph connects the `i`-th entry in `y` to the `j`-th entry in `x`.
+"""
+function pattern(f!, y, ::Type{T}, x) where {T<:AbstractTracer}
+    xt = trace_input(T, x)
+    yt = similar(y, T)
+    f!(yt, xt)
+    return _pattern(xt, yt)
+end
+
+_pattern(xt::AbstractTracer, yt::Number) = _pattern([xt], [yt])
+_pattern(xt::AbstractTracer, yt::AbstractArray{Number}) = _pattern([xt], yt)
+_pattern(xt::AbstractArray{<:AbstractTracer}, yt::Number) = _pattern(xt, [yt])
+function _pattern(xt::AbstractArray{<:AbstractTracer}, yt::AbstractArray{<:Number})
+    return _pattern_to_sparsemat(xt, yt)
+end
+
+function _pattern_to_sparsemat(
+    xt::AbstractArray{<:AbstractTracer}, yt::AbstractArray{<:Number}
+)
+    # Construct matrix of size (ouput_dim, input_dim)
+    n, m = length(xt), length(yt)
+    I = UInt64[]
+    J = UInt64[]
+    V = Bool[]
+    for (i, y) in enumerate(yt)
+        if y isa AbstractTracer
+            for j in inputs(y)
+                push!(I, i)
+                push!(J, j)
+                push!(V, true)
+            end
+        end
+    end
+    return sparse(I, J, V, m, n)
+end
diff --git a/src/tracer.jl b/src/tracer.jl
deleted file mode 100644
index cee0c7d7..00000000
--- a/src/tracer.jl
+++ /dev/null
@@ -1,123 +0,0 @@
-"""
-    Tracer(indexset) <: Number
-
-Number type keeping track of input indices of previous computations.
-
-See also the convenience constructor [`tracer`](@ref).
-For a higher-level interface, refer to [`connectivity`](@ref).
-
-## Examples
-By enumerating inputs with tracers, we can keep track of input connectivities:
-```jldoctest
-julia> xt = [tracer(1), tracer(2), tracer(3)]
-3-element Vector{Tracer}:
- Tracer(1,)
- Tracer(2,)
- Tracer(3,)
-
-julia> f(x) = [x[1]^2, 2 * x[1] * x[2]^2, sin(x[3])];
-
-julia> yt = f(xt)
-3-element Vector{Tracer}:
-   Tracer(1,)
- Tracer(1, 2)
-   Tracer(3,)
-```
-
-This works by overloading operators to either keep input connectivities constant, 
-compute unions or set connectivities to zero:
-```jldoctest Tracer
-julia> x = tracer(1, 2, 3)
-Tracer(1, 2, 3)
-
-julia> sin(x)  # Most operators don't modify input connectivities.
-Tracer(1, 2, 3)
-
-julia> 2 * x^3
-Tracer(1, 2, 3)
-
-julia> zero(x) # Tracer is strictly operator overloading... 
-Tracer()
-
-julia> 0 * x   # ...and doesn't look at input values.
-Tracer(1, 2, 3)
-
-julia> y = tracer(3, 5)
-Tracer(3, 5)
-
-julia> x + y   # Operations on two Tracers construct union sets
-Tracer(1, 2, 3, 5)
-
-julia> x ^ y
-Tracer(1, 2, 3, 5)
-```
-
-[`Tracer`](@ref) also supports random number generation and pre-allocations:
-```jldoctest Tracer
-julia> M = rand(Tracer, 3, 2)
-3×2 Matrix{Tracer}:
- Tracer()  Tracer()
- Tracer()  Tracer()
- Tracer()  Tracer()
-
-julia> similar(M)
-3×2 Matrix{Tracer}:
- Tracer()  Tracer()
- Tracer()  Tracer()
- Tracer()  Tracer()
-
-julia> M * [x, y]
-3-element Vector{Tracer}:
- Tracer(1, 2, 3, 5)
- Tracer(1, 2, 3, 5)
- Tracer(1, 2, 3, 5)
-```
-"""
-struct Tracer <: Number
-    inputs::BitSet # indices of connected, enumerated inputs
-end
-
-const EMPTY_TRACER = Tracer(BitSet())
-
-# We have to be careful when defining constructors:
-# Generic code expecting "regular" numbers `x` will sometimes convert them 
-# by calling `T(x)` (instead of `convert(T, x)`), where `T` can be `Tracer`.
-# When this happens, we create a new empty tracer with no input connectivity.
-Tracer(::Number)  = EMPTY_TRACER
-Tracer(t::Tracer) = t
-
-uniontracer(a::Tracer, b::Tracer) = Tracer(union(a.inputs, b.inputs))
-
-"""
-    tracer(index)
-    tracer(indices)
-
-Convenience constructor for [`Tracer`](@ref) from input indices.
-"""
-tracer(index::Integer) = Tracer(BitSet(index))
-tracer(inds::NTuple{N,<:Integer}) where {N} = Tracer(BitSet(inds))
-tracer(inds...)                             = tracer(inds)
-
-# Utilities for accessing input indices
-"""
-    inputs(tracer)
-
-Return raw `UInt64` input indices of a [`Tracer`](@ref).
-
-## Example
-```jldoctest
-julia> t = tracer(1, 2, 4)
-Tracer(1, 2, 4)
-
-julia> inputs(t)
-3-element Vector{Int64}:
- 1
- 2
- 4
-```
-"""
-inputs(t::Tracer) = collect(t.inputs)
-
-function Base.show(io::IO, t::Tracer)
-    return Base.show_delim_array(io, inputs(t), "Tracer(", ',', ')', true)
-end
diff --git a/src/tracers.jl b/src/tracers.jl
new file mode 100644
index 00000000..c932e492
--- /dev/null
+++ b/src/tracers.jl
@@ -0,0 +1,113 @@
+#==============#
+# Connectivity #
+#==============#
+
+"""
+    ConnectivityTracer(indexset) <: Number
+
+Number type keeping track of input indices of previous computations.
+
+See also the convenience constructor [`tracer`](@ref).
+For a higher-level interface, refer to [`pattern`](@ref).
+"""
+struct ConnectivityTracer <: AbstractTracer
+    inputs::BitSet # indices of connected, enumerated inputs
+end
+
+function Base.show(io::IO, t::ConnectivityTracer)
+    return Base.show_delim_array(io, inputs(t), "ConnectivityTracer(", ',', ')', true)
+end
+
+const EMPTY_CONNECTIVITY_TRACER = ConnectivityTracer(BitSet())
+
+# We have to be careful when defining constructors:
+# Generic code expecting "regular" numbers `x` will sometimes convert them 
+# by calling `T(x)` (instead of `convert(T, x)`), where `T` can be `ConnectivityTracer`.
+# When this happens, we create a new empty tracer with no input pattern.
+ConnectivityTracer(::Number) = EMPTY_CONNECTIVITY_TRACER
+ConnectivityTracer(t::ConnectivityTracer) = t
+
+#==========#
+# Jacobian #
+#==========#
+
+"""
+    JacobianTracer(indexset) <: Number
+
+Number type keeping track of input indices of previous computations with non-zero derivatives.
+
+See also the convenience constructor [`tracer`](@ref).
+For a higher-level interface, refer to [`pattern`](@ref).
+"""
+struct JacobianTracer <: AbstractTracer
+    inputs::BitSet # indices of connected, enumerated inputs
+end
+
+function Base.show(io::IO, t::JacobianTracer)
+    return Base.show_delim_array(io, inputs(t), "JacobianTracer(", ',', ')', true)
+end
+
+const EMPTY_JACOBIAN_TRACER = JacobianTracer(BitSet())
+
+JacobianTracer(::Number) = EMPTY_JACOBIAN_TRACER
+JacobianTracer(t::JacobianTracer) = t
+
+#===========#
+# Utilities #
+#===========#
+
+## Access inputs
+"""
+    inputs(tracer)
+
+Return raw `UInt64` input indices of a [`ConnectivityTracer`](@ref) or [`JacobianTracer`](@ref)
+
+## Example
+```jldoctest
+julia> t = tracer(ConnectivityTracer, 1, 2, 4)
+ConnectivityTracer(1, 2, 4)
+
+julia> inputs(t)
+3-element Vector{Int64}:
+ 1
+ 2
+ 4
+```
+"""
+inputs(t::ConnectivityTracer) = collect(t.inputs)
+inputs(t::JacobianTracer) = collect(t.inputs)
+
+## Unions of tracers
+function uniontracer(a::ConnectivityTracer, b::ConnectivityTracer)
+    return ConnectivityTracer(union(a.inputs, b.inputs))
+end
+
+function uniontracer(a::JacobianTracer, b::JacobianTracer)
+    return JacobianTracer(union(a.inputs, b.inputs))
+end
+
+## Get empty tracer
+empty(::JacobianTracer)           = EMPTY_JACOBIAN_TRACER
+empty(::Type{JacobianTracer})     = EMPTY_JACOBIAN_TRACER
+empty(::ConnectivityTracer)       = EMPTY_CONNECTIVITY_TRACER
+empty(::Type{ConnectivityTracer}) = EMPTY_CONNECTIVITY_TRACER
+
+"""
+    tracer(JacobianTracer, index)
+    tracer(JacobianTracer, indices)
+    tracer(ConnectivityTracer, index)
+    tracer(ConnectivityTracer, indices)
+
+Convenience constructor for [`JacobianTracer`](@ref) [`ConnectivityTracer`](@ref) from input indices.
+"""
+tracer(::Type{JacobianTracer}, index::Integer) = JacobianTracer(BitSet(index))
+tracer(::Type{ConnectivityTracer}, index::Integer) = ConnectivityTracer(BitSet(index))
+
+function tracer(::Type{JacobianTracer}, inds::NTuple{N,<:Integer}) where {N}
+    return JacobianTracer(BitSet(inds))
+end
+function tracer(::Type{ConnectivityTracer}, inds::NTuple{N,<:Integer}) where {N}
+    return ConnectivityTracer(BitSet(inds))
+end
+
+tracer(::Type{T}, inds...) where {T<:AbstractTracer} = tracer(T, inds)
diff --git a/test/benchmark.jl b/test/benchmark.jl
index 5b614e16..c98db653 100644
--- a/test/benchmark.jl
+++ b/test/benchmark.jl
@@ -19,7 +19,7 @@ function benchmark_brusselator(N::Integer, method=:tracer)
     f!(du, u) = brusselator_2d_loop(du, u, p, nothing)
 
     if method == :tracer
-        return @benchmark connectivity($f!, $du, $u)
+        return @benchmark pattern($f!, $du, $u)
     elseif method == :symbolics
         return @benchmark Symbolics.jacobian_sparsity($f!, $du, $u)
     end
@@ -31,7 +31,7 @@ function benchmark_conv(method=:tracer)
     f(x) = conv(x, w)
 
     if method == :tracer
-        return @benchmark connectivity($f, $x)
+        return @benchmark pattern($f, $x)
     elseif method == :symbolics
         return @benchmark Symbolics.jacobian_sparsity($f, $x)
     end
diff --git a/test/references/connectivity/Brusselator.txt b/test/references/pattern/connectivity/Brusselator.txt
similarity index 100%
rename from test/references/connectivity/Brusselator.txt
rename to test/references/pattern/connectivity/Brusselator.txt
diff --git a/test/references/connectivity/NNlib/conv.txt b/test/references/pattern/connectivity/NNlib/conv.txt
similarity index 100%
rename from test/references/connectivity/NNlib/conv.txt
rename to test/references/pattern/connectivity/NNlib/conv.txt
diff --git a/test/references/pattern/jacobian/Brusselator.txt b/test/references/pattern/jacobian/Brusselator.txt
new file mode 100644
index 00000000..24a82b43
--- /dev/null
+++ b/test/references/pattern/jacobian/Brusselator.txt
@@ -0,0 +1 @@
+Bool[1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0; 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0; 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0; 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0; 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0; 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0; 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1; 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0; 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0; 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0; 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0; 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0; 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1; 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1]
\ No newline at end of file
diff --git a/test/references/pattern/jacobian/NNlib/conv.txt b/test/references/pattern/jacobian/NNlib/conv.txt
new file mode 100644
index 00000000..aaf436e1
--- /dev/null
+++ b/test/references/pattern/jacobian/NNlib/conv.txt
@@ -0,0 +1 @@
+Bool[1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0; 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0; 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0; 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1]
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 7853d8e8..3217f9d2 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -37,19 +37,22 @@ DocMeta.setdocmeta!(
     @testset "JET tests" begin
         JET.test_package(SparseConnectivityTracer; target_defined_modules=true)
     end
-    @testset verbose = true "Classification of operators by diff'ability" begin
+    @testset "Doctests" begin
+        Documenter.doctest(SparseConnectivityTracer)
+    end
+    @testset "Classification of operators by diff'ability" begin
         include("test_differentiability.jl")
     end
     @testset "Connectivity" begin
         x = rand(3)
-        xt = trace_input(x)
+        xt = trace_input(ConnectivityTracer, x)
 
         # Matrix multiplication
         A = rand(1, 3)
         yt = only(A * xt)
         @test inputs(yt) == [1, 2, 3]
 
-        @test connectivity(x -> only(A * x), x) ≈ [1 1 1]
+        @test pattern(x -> only(A * x), ConnectivityTracer, x) ≈ [1 1 1]
 
         # Custom functions
         f(x) = [x[1]^2, 2 * x[1] * x[2]^2, sin(x[3])]
@@ -58,17 +61,29 @@ DocMeta.setdocmeta!(
         @test inputs(yt[2]) == [1, 2]
         @test inputs(yt[3]) == [3]
 
-        @test connectivity(f, x) ≈ [1 0 0; 1 1 0; 0 0 1]
+        @test pattern(f, ConnectivityTracer, x) ≈ [1 0 0; 1 1 0; 0 0 1]
+        @test pattern(f, JacobianTracer, x) ≈ [1 0 0; 1 1 0; 0 0 1]
+
+        @test pattern(identity, ConnectivityTracer, rand()) ≈ [1;;]
+        @test pattern(identity, JacobianTracer, rand()) ≈ [1;;]
+        @test pattern(Returns(1), ConnectivityTracer, 1) ≈ [0;;]
+        @test pattern(Returns(1), JacobianTracer, 1) ≈ [0;;]
 
-        @test connectivity(identity, rand()) ≈ [1;;]
-        @test connectivity(Returns(1), 1) ≈ [0;;]
+        # Test JacobianTracer on functions with zero derivatives
+        x = rand(2)
+        g(x) = [x[1] * x[2], ceil(x[1] * x[2]), x[1] * round(x[2])]
+        @test pattern(g, ConnectivityTracer, x) ≈ [1 1; 1 1; 1 1]
+        @test pattern(g, JacobianTracer, x) ≈ [1 1; 0 0; 1 0]
     end
     @testset "Real-world tests" begin
         @testset "NNlib" begin
             x = rand(3, 3, 2, 1) # WHCN
             w = rand(2, 2, 2, 1) # Conv((2, 2), 2 => 1)
-            C = connectivity(x -> NNlib.conv(x, w), x)
-            @test_reference "references/connectivity/NNlib/conv.txt" BitMatrix(C)
+            C = pattern(x -> NNlib.conv(x, w), ConnectivityTracer, x)
+            @test_reference "references/pattern/connectivity/NNlib/conv.txt" BitMatrix(C)
+            J = pattern(x -> NNlib.conv(x, w), JacobianTracer, x)
+            @test_reference "references/pattern/jacobian/NNlib/conv.txt" BitMatrix(J)
+            @test C == J
         end
         @testset "Brusselator" begin
             include("brusselator.jl")
@@ -85,8 +100,11 @@ DocMeta.setdocmeta!(
             du = similar(u)
             f!(du, u) = brusselator_2d_loop(du, u, p, nothing)
 
-            C = connectivity(f!, du, u)
-            @test_reference "references/connectivity/Brusselator.txt" BitMatrix(C)
+            C = pattern(f!, du, ConnectivityTracer, u)
+            @test_reference "references/pattern/connectivity/Brusselator.txt" BitMatrix(C)
+            J = pattern(f!, du, JacobianTracer, u)
+            @test_reference "references/pattern/jacobian/Brusselator.txt" BitMatrix(J)
+            @test C == J
 
             C_ref = Symbolics.jacobian_sparsity(f!, du, u)
             @test C == C_ref
@@ -95,7 +113,4 @@ DocMeta.setdocmeta!(
     @testset "ADTypes integration" begin
         include("adtypes.jl")
     end
-    @testset "Doctests" begin
-        Documenter.doctest(SparseConnectivityTracer)
-    end
 end