# Deterministic design of experiments¶

In this example we present the available deterministic design of experiments.

Four types of deterministic design of experiments are available:

• Axial

• Factorial

• Composite

• Box

Each type of deterministic design is discretized differently according to a number of levels.

Functionally speaking, a design is a Sample that lies within the unit cube and can be scaled and moved to cover the desired box.

```import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt

ot.Log.Show(ot.Log.NONE)
```

We will use the following function to plot bi-dimensional samples.

```def drawBidimensionalSample(sample, title):
n = sample.getSize()
graph = ot.Graph("%s, size=%d" % (title, n), "X1", "X2", True, "")
cloud = ot.Cloud(sample)
return graph
```

## Axial design¶

```levels = [1.0, 1.5, 3.0]
experiment = ot.Axial(2, levels)
sample = experiment.generate()
graph = drawBidimensionalSample(sample, "Axial")
view = viewer.View(graph)
```

Scale and to get desired location.

```sample *= 2.0
sample += [5.0, 8.0]
graph = drawBidimensionalSample(sample, "Axial")
view = viewer.View(graph)
```

## Factorial design¶

```experiment = ot.Factorial(2, levels)
sample = experiment.generate()
sample *= 2.0
sample += [5.0, 8.0]
graph = drawBidimensionalSample(sample, "Factorial")
view = viewer.View(graph)
```

## Composite design¶

```experiment = ot.Composite(2, levels)
sample = experiment.generate()
sample *= 2.0
sample += [5.0, 8.0]
graph = drawBidimensionalSample(sample, "Composite")
view = viewer.View(graph)
```

## Grid design¶

```levels = [3, 4]
experiment = ot.Box(levels)
sample = experiment.generate()
sample *= 2.0
sample += [5.0, 8.0]
graph = drawBidimensionalSample(sample, "Box")
view = viewer.View(graph)
plt.show()
```