2. Hailstone numbers

A sequence is called a hailstone sequence because the values typically rise and fall, somewhat analogously to a hailstone inside a cloud.

See working app at: https://pc-hailstone-numbers.anvil.app

2.1. References

  1. https://www.omnicalculator.com/math/collatz-conjecture

  2. https://www.dcode.fr/collatz-conjecture

  3. https://goodcalculators.com/collatz-conjecture-calculator/

  4. https://en.wikipedia.org/wiki/Collatz_conjecture

2.2. Design

Use a Column panel.
Use 3 label fields to display the information content.
Add a text box for the start number.
Add a button to generate the hailstone numbers.
Add a text area to display the hailstone numbers.
../_images/Hailstone_numbers.png

2.3. Get started

  1. Go to: https://anvil.works/new-build

  2. Click: Blank App.

  3. Choose: Material Design

2.4. Settings

  1. Click on the cog icon to show the settings tab.

  2. Enter an App name. Hailstone_numbers

  3. Enter an App title. Hailstone_numbers

  4. Enter an App description. Hailstone_numbers are a sequence of odd and even positive integers.

  5. Close the settings tab.

2.5. Build interface

2.5.1. Title

Drag and drop a label component onto the Drop title here container.
In the properties panel: name section, set the name to title.
In the properties panel: text section, set the text to Hailstone numbers.
In the properties panel: text section, set the font_size to 24.

2.5.2. Column panel

Drag and drop a column panel component onto the form.

2.5.3. Info

Drag and drop a label component onto the column panel.
In the properties panel: name section, set the name to info.
In the properties panel: text section, set the font_size to 18.
In the properties panel: text section, set the text to the text below.
Hailstone numbers are a sequence of odd and even positive integers.
The values typically rise and fall, like a hailstone inside a cloud.
e.g. 6, 3, 10, 5, 16, 8, 4, 2, 1

2.5.4. Rules

Drag and drop a label component onto the column panel to the right of the info label.
In the properties panel: name section, set the name to rules.
In the properties panel: text section, set the font_size to 18.
In the properties panel: text section, set the text to the text below.
The rules for producing hailstone numbers:
* Start with a positive whole number (integer)
* If the number is even, divide by 2.
* If the number is odd, multiply by 3 and add 1.
* Repeat for each new number and continue till 1 is reached.

2.5.5. Directions

Drag and drop a label component onto the column panel.
In the properties panel: name section, set the name to directions.
In the properties panel: text section, set the font_size to 18.
In the properties panel: text section, set the text to the text below.
Enter the start number (positive integer) and click Generate.

2.5.6. Hailstone_start

Drag and drop a TextBox component onto the column panel.
In the properties panel: name section, set the name to hailstone_start.
In the properties panel: properties section, set the placeholder to start number.
In the properties panel: properties section, set the type to number.
In the properties panel: text section, set the font_size to 24.
In the properties panel: Events section, click on the blue icon to the right of the pressed_enter label.
This will add a default script, hailstone_start_pressed_enter, to the code. This will be coded later with the Generate button code.

2.5.7. Generate_hailstone button

Drag and drop a Button component onto the column panel to the right of the hailstone_start textbox.
In the properties panel: name section, set the name to generate_hailstones.
In the properties panel: text section, set the font_size to 16.
In the properties panel: text section, set the text to Generate.
In the properties panel: appearance section, set the role to primary-color.
In the properties panel: icon section, set the icon to fa:star-o.
In the properties panel: Events section, click on the blue icon to the right of the click label.
This will add a default script, generate_click, to the code. This will be coded later to generate the hailstone numbers.

2.5.8. Error field

Drag and drop a label component onto the column panel below the start number textbox.
In the properties panel: name section, set the name to error.
In the properties panel: text section, set the font_size to 16.
In the properties panel: appearance section, set the foreground_color to #ff0000.
In the properties panel: icon section, set the icon to fa:exclamation-triangle.
../_images/Hailstone_error.png

2.5.9. Length_label

Drag and drop a label component onto the column panel.
In the properties panel: name section, set the name to length_label.
In the properties panel: text section, set the font_size to 18.
In the properties panel: text section, set the text to Length:.

2.5.10. Length

Drag and drop a label component onto the column panel to the right of the length_label label.
Control click and drag the divider on the left of the label to the left to minimize the length_label.
In the properties panel: name section, set the name to length.
In the properties panel: text section, set the font_size to 18.
In the properties panel: text section, set the text to Length:.

2.5.11. Start_label

Drag and drop a label component onto the column panel.
In the properties panel: name section, set the name to start_label.
In the properties panel: text section, set the font_size to 24.
In the properties panel: text section, set the text to start:.

2.5.12. Hailstone_numbers

Drag and drop a TextArea component onto the column panel.
In the properties panel: name section, set the name to hailstone_numbers.
In the properties panel: text section, set the font_size to 24.
In the properties panel: properties section, set the placeholder to Hailstone numbers.

2.6. Initial Code

Hide the error field by setting its visible property to False.
Hide the length fields the and hailstone list field. Use a separate function for this with a pararmeter to set the visibility of each of the 3 fields: length_label, length, hailstone_numbers.
class Form1(Form1Template):

    def __init__(self, **properties):
        # Set Form properties and Data Bindings.
        self.init_components(**properties)
        # hide error field and output fields
        self.error.visible = False
        self.set_main_field_vis(False)

    def set_main_field_vis(self, vis_bool):
        self.length_label.visible = vis_bool
        self.length.visible = vis_bool
        self.hailstone_numbers.visible = vis_bool

2.7. Event Code

Both the button click and pressing enter need to generate the hailstone list.
Place self.generate() in the body of both functions.
def generate_click(self, **event_args):
    self.generate()

def hailstone_start_pressed_enter(self, **event_args):
    self.generate()

2.8. Hailstone Code

The hailstone function takes the parameter, num.
The list is set to this value: hailstone_list = [num].
The while num > 1: loop runs while num is greater than 1. If the num value is 1, the hailstone_list, [1], is immediatley returned.
In the while loop, the last value is checked, hailstone_list[-1]. If the last value is 1, then the hailstone_list is returned.
hailstone_list[-1] % 2 == 0 is used to check whether the last number is an even number.
If it is even, the last value is halved.
If it is odd, the last value is multiplied by three and 1 is added.
def hailstone(self, num):
    # return list of numbers
    hailstone_list = [num]
    while num > 1:
        if hailstone_list[-1] == 1:
            return hailstone_list
        else:
            if hailstone_list[-1] % 2 == 0:
                new_num = int(hailstone_list[-1] / 2)
            else:
                new_num = (hailstone_list[-1] * 3) + 1
            hailstone_list.append(new_num)
    return hailstone_list

2.9. Checking the input

The test_integer function checks the input, hailstone_start, and sets the hailstone_seed value if it is a positive integer.
If not, a string is returned to display in the error field.
def test_integer(self):
    # str(invalid entries) give the string 'None'
    if str(self.hailstone_start.text) == 'None':
        return "Invalid number."
    # invalid entries give False, so not False is True
    if not self.hailstone_start.text:
        return "Not a valid start number."
    # catch 0, negative ints and floats below 1
    if self.hailstone_start.text < 1:
        return "Enter a whole number above 0."
    # floats
    if self.hailstone_start.text != int(self.hailstone_start.text):
        return "Postitive Integers, not floats are needed."
    # have an int, no error
    return None

2.10. Generate Code

The generate function uses the test_integer and hailstone functions to get the hailstone list.
It also takes care of displaying any errors and displaying the hailstone values if they are generated.
def generate(self):
    # hide error and clear it
    self.error.visible = False
    self.error.text = ""
    # check for error and display it if present
    error = self.test_integer()
    if error:
        self.error.text = error
        self.error.visible = True
        self.length.text = ""
        self.hailstone_numbers.text = ""
        self.set_output_field_vis(False)
        return
    # continue if no error
    hns = self.hailstone(self.hailstone_start.text)
    self.hailstone_numbers.text = hns
    self.length.text = len(hns)
    self.set_output_field_vis(True)

def test_integer(self):
    # str(invalid entries) give the string 'None'
    if str(self.hailstone_start.text) == 'None':
        return "Invalid number."
    # invalid entries give False, so not False is True
    if not self.hailstone_start.text:
        return "Not a valid start number."
    # catch 0, negative ints and floats below 1
    if self.hailstone_start.text < 1:
        return "Enter a whole number above 0."
    # floats
    if self.hailstone_start.text != int(self.hailstone_start.text):
        return "Postitive Integers, not floats are needed."
    # have an int, no error
    return None

def hailstone(self, num):
    # return list of numbers
    hailstone_list = [num]
    while num > 1:
        if hailstone_list[-1] == 1:
            return hailstone_list
        else:
            if hailstone_list[-1] % 2 == 0:
                new_num = int(hailstone_list[-1] / 2)
            else:
                new_num = (hailstone_list[-1] * 3) + 1
            hailstone_list.append(new_num)
    return hailstone_list

2.11. Final Code

The full code is below.
from anvil import *
import anvil.tables as tables
import anvil.tables.query as q
from anvil.tables import app_tables

class Form1(Form1Template):

    def __init__(self, **properties):
        # Set Form properties and Data Bindings.
        self.init_components(**properties)
        # hide error field and output fields
        self.error.visible = False
        self.set_output_field_vis(False)

    def set_output_field_vis(self, vis_bool):
        self.length_label.visible = vis_bool
        self.length.visible = vis_bool
        self.hailstone_numbers.visible = vis_bool

    def hailstone_start_change(self, **event_args):
        if self.hailstone_start.text:
            self.hailstone_start.text = min(100000, self.hailstone_start.text)

    def generate_click(self, **event_args):
        self.generate()

    def hailstone_start_pressed_enter(self, **event_args):
        self.generate()

    def generate(self):
        # hide error and clear it
        self.error.visible = False
        self.error.text = ""
        # check for error and display it if present
        error = self.test_integer()
        if error:
            self.error.text = error
            self.error.visible = True
            self.length.text = ""
            self.hailstone_numbers.text = ""
            self.set_output_field_vis(False)
            return
        # continue if no error
        hns = self.hailstone(self.hailstone_start.text)
        self.hailstone_numbers.text = hns
        self.length.text = len(hns)
        self.set_output_field_vis(True)

    def test_integer(self):
        # str(invalid entries) give the string 'None'
        if str(self.hailstone_start.text) == 'None':
            return "Invalid number."
        # invalid entries give False, so not False is True
        if not self.hailstone_start.text:
            return "Not a valid start number."
        # catch 0, negative ints and floats below 1
        if self.hailstone_start.text < 1:
            return "Enter a whole number above 0."
        # floats
        if self.hailstone_start.text != int(self.hailstone_start.text):
            return "Postitive Integers, not floats are needed."
        # have an int, no error
        return None

    def hailstone(self, num):
        # return list of numbers
        hailstone_list = [num]
        while num > 1:
            if hailstone_list[-1] == 1:
                return hailstone_list
            else:
                if hailstone_list[-1] % 2 == 0:
                    new_num = int(hailstone_list[-1] / 2)
                else:
                    new_num = (hailstone_list[-1] * 3) + 1
                hailstone_list.append(new_num)
        return hailstone_list

Tasks

  1. Limit the initial input to under 100000.

Limit the initial input to under 100000.

def hailstone_start_change(self, **event_args):
    if self.hailstone_start.text:
        self.hailstone_start.text = min(100000, self.hailstone_start.text)

Tasks

  1. The longest sequence is 351 for hailstone(77031) for numbers <100,000. Find another hailstone number under 100000 with a sequence length over 200.

  2. Advanced: Create a list of multipliers to replace the 3 multiplier. Add a textbox to enable the user to enter the multiplier. Restrict the values to 1, 3, 5, 7 or 9. e.g 3, 5 or 1, 3, 7. Randomly choose form this list when generating each new number in the hailstone sequence.

The longest sequence is 351 for hailstone(77031) for numbers <100,000. Find another hailstone number under 100000 with a sequence length over 200.

Look at the sequence for hailstone(77031) and find the the next number under 100000. It has a sequence length of 206.

Advanced: Create a list of multipliers to replace the 3 multiplier. Add a textbox to enable the user to enter the multiplier. Restrict the values to 1, 3, 5, 7 or 9. e.g 3, 5 or 1, 3, 7. Randomly choose form this list when generating each new number in the hailstone sequence.

Working app at: https://pc-hailstone-random-multipliers.anvil.app

# code to allow random choice from a list

from random import choice

# code to insert in def generate(self):

def generate(self):
    ...
    # check for error in multiplier and display it if present
    error = self.test_multiplier()
    if error:
    self.error.text = error
    self.error.visible = True
    self.length.text = ""
    self.hailstone_numbers.text = ""
    self.set_output_field_vis(False)
    return
    ...

# code to text multiplier input

 def test_multiplier(self):
    try:
    multiplier_list = self.multiplier.text
    multiplier_list = multiplier_list.split(",")
    multiplier_list = [int(x) for x in multiplier_list if int(x) % 2 == 1 and int(x) < 10 and int(x) > 0]
    if len(multiplier_list) == 0:
        multiplier_list = [3]
        self.multiplier_list = multiplier_list
        self.multiplier.text = str(multiplier_list).strip('[]')
        print(self.multiplier.text)
        return None
    except ValueError as error:
        self.multiplier_list = None
        return "multiplier requires positive integers separated by commas."
    except IndexError as error:
        self.multiplier_list = None
        return "multiplier requires positive integers separated by commas."

# code to generate hailstone using **choice(self.multiplier_list)**

def hailstone(self, num):
    # return list of numbers
    hailstone_list = [num]
    while num > 1:
        if hailstone_list[-1] == 1:
            return hailstone_list
        else:
            if hailstone_list[-1] % 2 == 0:
                new_num = int(hailstone_list[-1] / 2)
            else:
                multiplier = choice(self.multiplier_list)
                new_num = (hailstone_list[-1] * multiplier) + 1
            hailstone_list.append(new_num)
            if len(hailstone_list) > 1000:
                return hailstone_list
    return hailstone_list