You could create Theissen polygons around your point data. Then, if you need them to be rasterized, rasterize them to a dataset with a fine spatial resolution.
Here is a link to Thiessen Polyons.
And conversion from Polygon to raster.
These tools require more ESRI advanced license levels and toolboxes that you may not have. If that is the case, look to ...
A raster is basically an image composed by pixels. Each pixel must have the same resolution (size) as all other pixels in the image. Also, they are placed in a regular grid made by rows and columns.
As such, you cannot have in the same image pixels that are not placed exactly inside this grid and which are not side by ...
There are two basic methods for displaying points that are too close together.
The first method is clustering. This method combines nearby points into a single symbol. The symbol often includes a number, which shows how many points have been combined. Here's a blog post about using point clustering symbology:
Picture below shows talweg, generated by using flood depth and flow paths derived by using Hydrology tools:
As one can see flow paths depict channel shape in a well defined valleys without depressions along it. If there is one, results are random.
What is happening on a flat terrain is absolutely out of control, your pictures illustrate this nicely. So in ...
Try to rename your C:\Users\YOUR_USER\Documents\ArcGIS folder and launch ArcMap to let it re-create it from scratch. In my case, it contains these folders/files:
If this works, either delete or keep the renamed folder: you won't need it anymore.
This has solved a totally different problem for me (in my case, I had the size of my MXDs being huge like ...