Collatz Conjecture in Eve

collatz.eve

# Collatz Conjecture
## Description
The Collatz Conjecture deals with an integer #`n` and the #`steps` it takes to reach 1.

```
commit
  [#n]
  [#step]
```

If #`n` is even, divide it by 2. If #`n` is odd, multiply it by 3 and add 1.

```eve
search
  n = [#n value > 1]
  m = mod[value: n.value, by: 2]
  next = if m = 0 then n.value / 2 else n.value * 3 + 1
    
commit
  n.value := next
  [#step from: n.value, to: next]
```

Does #`n` always converge to 1?
## User interface
Let the user change n

```eve
search @browser @event
  [#click element: [#button]] // remove me for a bug
  [#input name: "n", value: new]
  
search
  n = [#n]
  steps = [#step]

commit
  n.value := new
  steps := none
  [#step]
```

by changing this form

```eve
commit @browser
  [#label text: "Choose n to start: ", children:
    [#input type: "number" name: "n"]]
  [#button text: "Go"]
```

Show how many steps were required to converge.

```
search
  [#n value: n]
  steps = count[given:[#step]] - 1
  
bind @browser
  [#div sort: 1, text: "reached {{n}} in {{steps}} steps"]
```

Show the individual steps taken.

```
search
  [#step from to]
  
bind @browser
  [#div sort: 2, text: "{{from}} -> {{to}}"]
```