3. Fibonacci numbers
The Fibonacci sequence is a sequence of numbers in which each term of the sequence is equal to the sum of two preceding terms.
This way, each term can be expressed by this equation:
Fₙ = Fₙ₋₂ + Fₙ₋₁
The Fibonacci sequence typically has the first two terms equal to F₀ = 0 and F₁ = 1.
See working app at: ****************
3.1. References
3.2. Design
Use a Column panel.
Use 3 label fields to display the information content.
Add a text box for the term number.
Add a button to generate the fibonacci numbers.
Add a text area to display the fibonacci numbers.
3.3. Get started
Click: Blank App.
Choose: Material Design
3.4. Settings
Click on the cog icon to show the settings tab.
Enter an App name. Fibonacci_numbers
Enter an App title. Fibonacci_numbers
Enter an App description. Fibonacci_numbers are a sequence of odd and even positive integers.
Close the settings tab.
3.5. Build interface
3.5.1. 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 Fibonacci numbers.
In the properties panel: text section, set the font_size to 24.
3.5.2. Column panel
Drag and drop a column panel component onto the form.
3.5.3. 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.
Fibonacci numbers are a sequence of odd and even positive integers.
The values typically rise and fall, like a Fibonacci inside a cloud.
e.g. 6, 3, 10, 5, 16, 8, 4, 2, 1
3.5.4. 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.
3.5.5. 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.
3.5.6. Fibonacci_start
Drag and drop a TextBox component onto the column panel.
In the properties panel: name section, set the name to Fibonacci_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, Fibonacci_start_pressed_enter, to the code. This will be coded later with the Generate button code.
3.5.8. 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.
3.5.9. 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:.
3.5.10. 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:.
3.5.11. 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:.
3.5.12. Fibonacci_numbers
Drag and drop a TextArea component onto the column panel.
In the properties panel: name section, set the name to Fibonacci_numbers.
In the properties panel: text section, set the font_size to 24.
In the properties panel: properties section, set the placeholder to Fibonacci numbers.
3.6. Initial Code
Hide the error field by setting its visible property to False.
Hide the length fields the and Fibonacci list field. Use a separate function for this with a parameter to set the visibility of each of the 3 fields: length_label, length, Fibonacci_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.Fibonacci_numbers.visible = vis_bool
3.7. Event Code
Both the button click and pressing enter need to generate the Fibonacci list.
Place self.generate() in the body of both functions.
def generate_click(self, **event_args):
self.generate()
def Fibonacci_start_pressed_enter(self, **event_args):
self.generate()
3.8. Fibonacci Code
The Fibonacci function takes the parameter, num.
The list is set to this value: Fibonacci_list = [num].
The while num > 1: loop runs while num is greater than 1. If the num value is 1, the Fibonacci_list, [1], is immediately returned.
In the while loop, the last value is checked, Fibonacci_list[-1]. If the last value is 1, then the Fibonacci_list is returned.
Fibonacci_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 Fibonacci(self, num):
# return list of numbers
Fibonacci_list = [num]
while num > 1:
if Fibonacci_list[-1] == 1:
return Fibonacci_list
else:
if Fibonacci_list[-1] % 2 == 0:
new_num = int(Fibonacci_list[-1] / 2)
else:
new_num = (Fibonacci_list[-1] * 3) + 1
Fibonacci_list.append(new_num)
return Fibonacci_list
3.9. Checking the input
The test_integer function checks the input, Fibonacci_start, and sets the Fibonacci_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.Fibonacci_start.text) == 'None':
return "Invalid number."
# invalid entries give False, so not False is True
if not self.Fibonacci_start.text:
return "Not a valid start number."
# catch 0, negative ints and floats below 1
if self.Fibonacci_start.text < 1:
return "Enter a whole number above 0."
# floats
if self.Fibonacci_start.text != int(self.Fibonacci_start.text):
return "Positive Integers, not floats are needed."
# have an int, no error
return None
3.10. Generate Code
The generate function uses the test_integer and Fibonacci functions to get the Fibonacci list.
It also takes care of displaying any errors and displaying the Fibonacci 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.Fibonacci_numbers.text = ""
self.set_output_field_vis(False)
return
# continue if no error
hns = self.Fibonacci(self.Fibonacci_start.text)
self.Fibonacci_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.Fibonacci_start.text) == 'None':
return "Invalid number."
# invalid entries give False, so not False is True
if not self.Fibonacci_start.text:
return "Not a valid start number."
# catch 0, negative ints and floats below 1
if self.Fibonacci_start.text < 1:
return "Enter a whole number above 0."
# floats
if self.Fibonacci_start.text != int(self.Fibonacci_start.text):
return "Positive Integers, not floats are needed."
# have an int, no error
return None
def Fibonacci(self, num):
# return list of numbers
Fibonacci_list = [num]
while num > 1:
if Fibonacci_list[-1] == 1:
return Fibonacci_list
else:
if Fibonacci_list[-1] % 2 == 0:
new_num = int(Fibonacci_list[-1] / 2)
else:
new_num = (Fibonacci_list[-1] * 3) + 1
Fibonacci_list.append(new_num)
return Fibonacci_list
3.11. 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.Fibonacci_numbers.visible = vis_bool
def Fibonacci_start_change(self, **event_args):
if self.Fibonacci_start.text:
self.Fibonacci_start.text = min(100000, self.Fibonacci_start.text)
def generate_click(self, **event_args):
self.generate()
def Fibonacci_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.Fibonacci_numbers.text = ""
self.set_output_field_vis(False)
return
# continue if no error
hns = self.Fibonacci(self.Fibonacci_start.text)
self.Fibonacci_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.Fibonacci_start.text) == 'None':
return "Invalid number."
# invalid entries give False, so not False is True
if not self.Fibonacci_start.text:
return "Not a valid start number."
# catch 0, negative ints and floats below 1
if self.Fibonacci_start.text < 1:
return "Enter a whole number above 0."
# floats
if self.Fibonacci_start.text != int(self.Fibonacci_start.text):
return "Positive Integers, not floats are needed."
# have an int, no error
return None
def Fibonacci(self, num):
# return list of numbers
Fibonacci_list = [num]
while num > 1:
if Fibonacci_list[-1] == 1:
return Fibonacci_list
else:
if Fibonacci_list[-1] % 2 == 0:
new_num = int(Fibonacci_list[-1] / 2)
else:
new_num = (Fibonacci_list[-1] * 3) + 1
Fibonacci_list.append(new_num)
return Fibonacci_list
Tasks
Limit the initial input to under 100000.
Limit the initial input to under 100000.
def Fibonacci_start_change(self, **event_args):
if self.Fibonacci_start.text:
self.Fibonacci_start.text = min(100000, self.Fibonacci_start.text)
Tasks
The longest sequence is 351 for Fibonacci(77031) for numbers <100,000. Find another Fibonacci number under 100000 with a sequence length over 200.
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 Fibonacci sequence.
The longest sequence is 351 for Fibonacci(77031) for numbers <100,000. Find another Fibonacci number under 100000 with a sequence length over 200.
Look at the sequence for Fibonacci(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 Fibonacci sequence.
Working app at: https://pc-Fibonacci-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.Fibonacci_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 Fibonacci using **choice(self.multiplier_list)**
def Fibonacci(self, num):
# return list of numbers
Fibonacci_list = [num]
while num > 1:
if Fibonacci_list[-1] == 1:
return Fibonacci_list
else:
if Fibonacci_list[-1] % 2 == 0:
new_num = int(Fibonacci_list[-1] / 2)
else:
multiplier = choice(self.multiplier_list)
new_num = (Fibonacci_list[-1] * multiplier) + 1
Fibonacci_list.append(new_num)
if len(Fibonacci_list) > 1000:
return Fibonacci_list
return Fibonacci_list